How does one explain consistency within phenomena if the mind generates phenomena?

It is likely that the quote you are referring to is

all conditioned dharma
are like dreams, illusions,
bubbles, shadows,
Like dew drops (in the morning sun),
or a lightening flash,
contemplate them thus.

All sentient beings have Buddha Nature. Wisdom realizing the holy state of Emptiness and Compassion for all sentient beings uniting.

The above gatha is part of the Diamond Cutter or Vajra Cutter sutra.

Contemplation of the above gatha is one of the most amazing actions one can pursue in their lifetime! Happy you chose this one to investigate.

Please read about the benefits here: http://www.lamayeshe.com/advice/diamond-cutter-sutra

And please see the direct resource (Vajra Cutter Sutra) via the Tibetan lineages http://cdn.fpmt.org/wp-content/uploads/sutras/vajra_cutter_sutra_c5.pdf?4320b0

Or this resource (the first one I came across)

http://www.buddhanet.net/pdf_file/prajparagen2.pdf

Any phenomena we know about the world is what we have sensed through our sense faculties. If we cannot sense any phenomena there will be no way we can know about it.

The definition of mind is the process to experience and object or phenomena, or to know what is felt through contact.

So when you experience something many of what you see is pieced together from multiple experiences you get and your part memory of how you classified these experiences. So the picture of reality you piece together is not the most accurate.

what is the Buddhist explanation?

You're reading the Laṅkāvatāra Sūtra.

I'd like to mention just in case you don't know already that there are different schools of Buddhism, spread over centuries and continents. They have much in common and later schools evolve from earlier schools. To the extent that they're similar, it makes sense to ask about "the" Buddhist explanation.

The Laṅkāvatāra Sūtra is apparently important to the early Zen school.

This edition by Guṇabhadra is said to be the one handed down from the founder of Chan Buddhism, Bodhidharma, to the Second Patriarch, Dazu Huike, saying:

I have here the Laṅkāvatāra in four fascicles which I now pass to you. It contains the essential teaching concerning the mind-ground of the Tathagata, by means of which you lead all sentient beings to the truth of Buddhism

Essentially that all we touch, see, taste, hear, and feel is no more real than a dream.

Beware that it's some kind of analogy or metaphor: and don't take that analogy too far.

For example if something were "like an apple", by that I might mean that it's round, sweet, portable, grows on trees, and/or etc.; but that doesn't mean it's exactly like an apple in all respects.

You've focused on one aspect of "dream": i.e. that a dream is irrational, private, irreproducible, and/or not shareable ... but that's not necessarily what the suttra intended when it mentioned "dream".

There's another translation of the sutra here (by D. T. Suzuki), which begins with an explanation/commentary which you might like to read in detail.

Part of it says,

Thus, according to Buddhist philosophy, reality must be grasped in this world and by this world, for it is that "Beyond which is also Within". The Lanka compares it to the moon in water or a flower in a mirror. It is within and yet outside, it is outside and yet within. This aspect of reality is described as "unobtainable" or "unattainable" (anupalabdha). And just because it is unobtainable in a world of particulars, the latter from the point of view of reality is like a dream, like a mirage, and so on. The subtlest relation of reality to the world is beyond description, it yields its secrets only to him who has actually realised it in himself by means of noble wisdom (aryajnana or prajna). This realisation is also a kind of knowledge though different from what is generally known by this name.

When I read that, I think it's saying that we don't understand or perceive the world very well. We perceive the world as in a dream, analogous to perceiving the moon's reflection in water:

It doesn't imply that the moon is unreal or a dream, and doesn't imply that two people won't both see a reflection of the moon.

Another impression I get from that description of "unobtainable" is, sometimes you might dream that are you are with someone, that you are somewhere, that you have something ... but then when you wake up you realize, "I do not, now in waking reality, have that person or place or thing, it was just a dream". Similarly perhaps they're saying that, in just the same way, even in waking reality we don't really "have" things, things are unattainable (but I don't know why: perhaps I guess it's because all we really have are our mind-made internal sense-impressions; or perhaps it's because the having of things is impermanent and in that way dreamlike; or perhaps because we ourselves e.g. in the sense that "I have a self" are dreams).

Some of the other answers to this question are based on the perspective of earlier schools of Buddhism.

I suspect this text (or the doctrine described in this text, or the school whose doctrine is described in this text) doesn't exactly contradict those answers but it has added concepts such as "non-dualism" which I don't think are so explicit/emphasized in earlier texts/schools.

Reading more Suzuki's introduction, it says,

In considering the theory of Mind-only, we have to be careful not to understand this term psychologically.

I don't know what that means but there is a "mind-only" school e.g. mentioned in this answer, "Why is the Yogācāra school called 'mind only'?", and elsewhere.

I was wondering how Suzuki would translate "dream" but when I get into Chapter 1 of his translation I find that his translation (or the his version of the sutra which he's translating) is entirely missing e.g. the first of the sentences which contains the word "dream" in the edition which you're reading.

I’d just like to add some general comments to your - excellent - question.

First of all, your question is not specifically Buddhist. If you take a look at the history of philosophy of science, this is a major problem and has been answered in many different ways. And the greatest philosophers of all times all more or less agree that we cannot have absolute knowledge about the ultimate reality - that's only for the enlightened minds.

My comments are purely Buddhist.

One is about karma, the other is about the idea that we can be mistaken but at the same time have reliable knowledge.

Karma

If consistency does exist then is there really only one mind?

We are humans, with human karma and human minds. When we observe the world and its causal regularity and unity, our observations are reflections of our karmic dispositions. An example is that when we see a river flowing before us, we see water. But the heavenly beings see it as heavenly nectar. Hungry ghosts see it as pus and blood. Fish see the river as their palace. And all of them are right, from their perspective. For example a termite sees a stick of wood as “food” or “a world of food” , whereas we humans see it as a stick of wood. And both are correct – conventionally. And this brings me to the other point.

We can be mistaken, but have reliable information about the conventional world.

how is it possible that everyone agrees upon laws of physics and mathematical truths? Doesn't consistency among observers imply an external reality independent of the mind?

Ultimately the laws of physics are not true. They are regularities and conventionalities for certain minds of certain perspectives. This is not because we have agreed upon it between humans, but because of our karmic dispositions this is the way the world appears to us all. We are not enlightened. As we deepen our understanding of emptiness, we grow increasingly to distrust and to disbelieve this false appearance, but the false appearance remains until we are enlightened. This is a strange truth, and it is the crux of the matter: we have from our senses reliable information about the ordinary things in the world even though our senses are at the same time deceived about just how these things really exist. It is an interesting fact that researchers in the field of quantum mechanics are coming to the same conclusions.

Our eyes and ears are “mistaken” but not “wrong”. They are reliable sources yet mistaken because they are constantly presenting images of their objects as existing substantially, naturally, independently.

In this sense we are dreaming.

Basically, the Buddhist approach to understanding reality is for each one of us to aim our attention at our individual present moment experience. This is "experiencial reality", meaning we need to experience it to understand it.

We really don't need to even read books to understand the Buddhist approach because practicing experiencing present moment reality is what brings the understanding we are really looking for. All the suttas and dharma that we need to study is only to guide us to the real way of getting understanding. This is why people who only study the teachings of the Buddha and do not practice them do not really live by the Dhamma as the Buddha says.

It doesn't matter that the material universe has it's own system of rules or physics because we aren't practicing in a material or conceptual reality but in our own moment by moment experiencial reality that really exists. The future, past, material world and all rules human made or human discovered are all conceptual. Conceptual reality is all being decided on and assumed about by our minds and so conceptual reality is a product of mind not reality.

When practicing with the Buddha's approach to reality, whatever an individual is experiencing in the present moment is all that is.

There are four paramattha dhammas meaning "ultimate realities" or things that are atomic meaning they cannot get any smaller. They are citta(mind), cetasika(mind objects), rūpa(matter) and nibbana.

Citta, Cetasika, Rupa, Nibbana are the four ultimate realities. Everything else is just conventional or conceptual truths.

When you see the moon, it's basically the eyes sensing the secondary rupa called Vanna. There's no moon in the ultimate reality. Moon is just what the mind fabricates when rupa meets the eyes.

There's consistency because human senses are similar. Other animals see things differently compared to humans. Imagine what the world would look like if we had microscopic eyes.

Saying all phenomena are mind made is similar to saying that all pottery is made by a potter. Pottery is just clay in reality. But the potter(mind) shapes the clay into different objects.

When you start dreaming, it is not Rupa that is perceived by the mind. It's another thought or a memory perceived by the mind. So it is a fabrication of a fabrication. That has a higher chance of being inconsistent. But it is not unlikely that 2 people dream of the same object in the same way. And it is not unlikely that 2 people see the same object differently even when the senses are similar. One person might see a beautiful woman, but a meditative monk might see her as a skeleton:

"Reverend sir, have you seen a woman pass this way?"
 And the elder said:

"Was it a woman, or a man,
That passed this way? I cannot tell.
But this I know, a set of bones
Is traveling on upon this road."

if consistency does exist then is there really only one mind? Or are there many? If there are many then how can consistency be satisfied?

Does a mango tree always give mangoes when fruiting? Or can it give apples as well? So if a mango tree always give mango fruits, should all the mangoes in the world come from one tree? Or can there be many mango trees?

Laws of physics are formulated by observing and hypothesizing. There's no direct knowledge involved. If laws of physics are ultimate reality, why do they change with time? Hypotheses are clearly mind made.

So is mathematics. ex: 1 is an agreement and 1 + 1 = 2 is a concept based on that agreement.

I too had this question for a long time. Then I read Gil Fronsdal's translation of the Dhammapada, which begins (emphasis mine):

All experience is preceded by mind,
Led by mind,
Made by mind.

This use of the word experience, where phenomena is often used, is much more accessible. Remember, the Buddha did not say "all phenomena is made by mind"; he said "manopubbaṅgamā dhammā manoseṭṭhā manomayā". To say that much can be lost in translation would be an understatement.

I prefer Gil's translation of experience because it fits with what makes sense. It's not everything that exists in our mind, but how we experience everything.

Consider a simple example. If you and I stand beside one another and together look at a houseplant in front of us, we will both see the houseplant. It's not that our minds are simultaneously (and coincidentally!) creating a houseplant that isn't really there; the plant is a real thing that exists in the world. But our minds will experience it differently: we'll interpret different shades of green, we'll consider the scent of the soil uniquely, and we may even have different emotional responses based on any memories associated with this particular kind of plant. The plant wasn't created by our minds, but every aspect of how we experience the plant was.

And remember the broader point that the Buddha was was making in that opening chapter, which continues:

Speak or act with a corrupted mind,
And suffering follows
As the wagon wheel follows the hoof of the ox.

The point wasn't that everything we experience comes from our minds, but that because the mind plays a critical role in how we experience everything, the state of our mind set the stage for how (or whether) we will experience any suffering.