Intention and Karma

Relying on what the Dalai Lama and Matthieu Ricard say is not a good idea. Those people fail to understand that sati, sati sampajanna, satipatthana are not ''just knowing what is happening right now'' but knowing the vedanas, sanna and vitakka plus cleaning them. The people who created vipassana mediation do the same mistake as the people who invented mahayana: they claim that tracking sense objects is ''living in the present moment'' and that tracking those stuff is meritorious, whereas the meritorious activity is actually cleaning vedanas, sanna and vitakkas (so this requires to actually track them in the first place). Plus you cannot clean rupa, kaya, the sense objects, the earth elements and so on, so tracking them and calling this meritorious is idiotic, that's the whole point of the buddha.

Then when vitakka is cleaned, there is the jhanas and the buddha calls this ''abiding in the here and now'' which is today called ''living in the present moment'' to use the word of the puthujjanas above. They confuse kāya-gatā-sati with tracking sense objects. This is why those people are bad at ''sense restrained'', because they are bad at the cultivatoin for ''sense restrained'', which is sati, which makes them fail at jhanas, let alone right samadhi, let alone disenchantment, dispassion and all that.

When a text (e.g. Abhidhamma) lists 'wholesome' mental factors, is it meant that these are also likely to produce positive karmic consequences, or that these are just beneficial in general?

I'm not sure i understand your distinction between karmic consequences, and what is beneficial in general. They seem like the same thing to me.

As well, from this answer I understand that karma refers specifically to the ethical intention. So, when their compassionate action which lacks wisdom produces detrimental effects, is a well-intended, compassionate person still nevertheless generating positive karma? This possibility seems to imply that developing a compassionate intention almost negates completely the possibility of unvirtuous karma.

In theory, we can have the best of intentions and still make a mess. A favorite (non-buddhist) quote of mine is "the road to hell is paved with good intentions".

Karma is a two sided coin. Our actions (karma) needs to be well meaning, as well as having good consequences (vipaka) in order to be considered beneficial.

(There are other aspects to take into consideration if one wishes to develop even more skillful karma-vipaka, but that's perhaps another topic).

Sati is mindfulness. It's keeping the mind on the task, without wandering.

From SN 47.20:

The Blessed One said, "Suppose, monks, that a large crowd of people comes thronging together, saying, 'The beauty queen! The beauty queen!' And suppose that the beauty queen is highly accomplished at singing & dancing, so that an even greater crowd comes thronging, saying, 'The beauty queen is singing! The beauty queen is dancing!' Then a man comes along, desiring life & shrinking from death, desiring pleasure & abhorring pain. They say to him, 'Now look here, mister. You must take this bowl filled to the brim with oil and carry it on your head in between the great crowd & the beauty queen. A man with a raised sword will follow right behind you, and wherever you spill even a drop of oil, right there will he cut off your head.' Now what do you think, monks: Will that man, not paying attention to the bowl of oil, let himself get distracted outside?"

"No, lord."

"I have given you this parable to convey a meaning. The meaning is this: The bowl filled to the brim with oil stands for mindfulness immersed in the body. Thus you should train yourselves: 'We will develop mindfulness immersed in the body. We will pursue it, hand it the reins and take it as a basis, give it a grounding, steady it, consolidate it, and undertake it well.' That is how you should train yourselves."

However, sati is not good enough. There is also samma sati - right mindfulness. Right mindfulness includes right view. Right view is the forerunner of the path according to MN 117.

From MN 117:

"One makes an effort for the abandoning of wrong view & for entering into right view: This is one's right effort. One is mindful to abandon wrong view & to enter & remain in right view: This is one's right mindfulness. Thus these three qualities — right view, right effort, & right mindfulness — run & circle around right view.

While sati or mindfulness is keeping the mind on the task, manasikara or attention is about directing the mind in the right direction.

Yoniso manasikara is appropriate attention and ayoniso manasikara is inappropriate attention. You can read the question "What is yoniso manasikara and ayoniso manasikara?"

From SN 9.11:

I have heard that on one occasion a certain monk was dwelling among the Kosalans in a forest thicket. Now at that time, he spent the day's abiding thinking evil, unskillful thoughts: i.e., thoughts of sensuality, thoughts of ill will, thoughts of doing harm.

Then the devata inhabiting the forest thicket, feeling sympathy for the monk, desiring his benefit, desiring to bring him to his senses, approached him and addressed him with this verse:

From inappropriate attention
you're being chewed by your thoughts. Relinquishing what's inappropriate,
contemplate appropriately.

Keeping your mind on the Teacher,
the Dhamma, the Sangha, your virtues,
you will arrive at
joy,
rapture,
pleasure
without doubt.

Then, saturated
with joy,
you will put an end
to suffering & stress.

The monk, chastened by the devata, came to his senses.

So, what does this mean? Both are needed - samma sati or right mindfulness, and yoniso manasikara or appropriate attention. However, samma ditthi or right view has to come first. Without right view, every other effort goes the wrong way.

The sniper who aims, shoots and kills another person, may be mindful and have attention, but he doesn't have right view, because a person with right view will stick heedfully (appamada) to the first precept and not kill others, especially another human being.

The sniper who aims, shoots and kills another person, may be mindful and have attention, but it's not right mindfulness and not appropriate attention.

Wholesome and unwholesome minds/types of consciousness, when ripen give rise to the respective resultant minds/types of consciousness. See: 89 / 121 types of consciousness

Sati in the The 52 Mental Factors (cetasika) is the Right Mindfulness. The mindfulness a shooter uses is Ekaggatā to concentrate the aim and Manasikāra as attention. These are universal factors which can appear in wholesome and unwholesome acts.

For example, in the Theravada tradition I read that sati, i.e. mindfulness, is a beautiful mental factor. In a discussion with the Dalai Lama, Matthieu Ricard explains how even a sniper may use mindfulness. So I am confused as to whether 'wholesome' and 'karmically positive' are synonymous or not.

This is where it's important to examine the root words in Pali. The English term 'mindfulness' is pretty broad and can carry different connotations depending on context, hence the need to look up its Pali terms to see the distinction. For example, in the case of unwholesome mindfulness of a sniper that Ven. Ricard was referring to, he possibly meant 'Manasikara'(or 'attention') instead of Sati. Manasikara is 1 of the 13 mental factors under the Annasamana(Ethically Variable) group; while Sati(or 'mindfulness') belongs to the Sobhana(Beautiful) group along with 25 other mental factors. All the details are pretty well-explained in Ven. Bodhi's "Comprehensive Manual of Abhidhamma"

Regarding actions that was done out of good intention but ended up with terrible results, this is exactly why Buddhism emphasizes the cultivation of both compassion and wisdom, which have to go hand in hand. So for example, some well-intent action that resulted in many accidental lives lost cannot be expected to reap some exclusively good kammic fruit. At best it'd only result in what's called mixed kamma with dark and bright results (ref. MN 57).