At what stage is it wrong to consider oneself wise?

To consider oneself wise is to possibly delude oneself as to the reality of a situation. Keep doubt, and your Personal Protection Equipment, handy at all times.

You are actually asking how to behave wisely and that is a very wise question.

Before answering that, please note that for wisdom at all stages, consider the ten qualities of an adept (DN33):

right view, right thought, right speech, right action, right livelihood, right effort, right mindfulness, right immersion, right knowledge, and right freedom.

Let us also agree that considering oneself anything at all is just perpetuating identity view (MN44).

And with regard to the "accomplishment of wisdom", we should also mention:

never be content with skillful qualities

To come back to your question on wise behavior, consider the three practices grouping (ethics, wisdom, immersion) of the noble eight-fold path DN44:

Right speech, right action, and right livelihood: these things are included in the category of ethics

Right view and right thought: these things are included in the category of wisdom

Right effort, right mindfulness, and right immersion: these things are included in the category of immersion

Right knowledge arises out of immersion (i.e., continue your practice). The arising of right knowledge takes time. Therefore, to guide your actions in the absence of right knowledge, simply observe the ethical precepts you have chosen. This is how the three practices support each other endlessly.

Seeing danger in the slightest flaw, keep the rules you’ve undertaken. MN6

And let mindfulness be the single guard of your heart. (DN33)

Tough question.

I wonder if it is a matter of relativity. Compared to some folk I'm completely sure I'm wise, compared to others I'm completely sure I'm not.

To be wise in something like an absolute sense would require a comprehensive understanding of reality. If one has this then it seems fine to consider oneself wise. After all, the masters all speak of cultivating wisdom and we should be able to know when we have cultivated it.

You say 'something more mundane, being wise and able to tell e.g. what is a fake way of behaving, or the difference between right and wrong.'

These are not mundane instances of wisdom. A deep understanding of the causes of behaviour and of the relationship between right and wrong would require a profound understanding of reality.

Whether it would be wise to consider ourselves wise would depend on whether we are wise, and if we are we'll know the answer. Yet there is a certain wisdom in the question so perhaps we would have to be at least a little wise to ask it.

Then again, to call the ability to tell right from wrong 'wisdom' may not be quite accurate. Lao Tsu tells us 'Because right and wrong appeared the Way was injured'. Perhaps wisdom is seeing the vacuity of the words 'right' and 'wrong' as absolute terms.

If for a moment I thought myself wise I would expect my wings to melt, but I'm happy to think I'm more nearly wise than I used to be. I see no harm in thinking yourself wiser than some or even than many, but if you attempt to explain exactly what you mean it may prove difficult.

You could ask someone at the Chicago Center for Practical Wisdom. A few more decades and they'll have defined the words.

Just thinking out loud. I'd say a wise person is one who knows whether it is wise to think themselves wise.

Is it always wrong to consider oneself wise?

To refer to yourself as wise could develop an over-inflated sense of self. I think it's best to just remain silent in mind and speech about the concepts you may want to use to describe yourself.

In the Diamond Sutra, Chapter 10 points this out thus:

“A disciple should develop a mind which is in no way dependent upon sights, sounds, smells, tastes, sensory sensations or any mental conceptions. A disciple should develop a mind which does not rely on anything.”

“Therefore, Subhuti, the minds of all disciples should be purified of all thoughts that relate to seeing, hearing, tasting, smelling, touching, and discriminating. They should use their minds spontaneously and naturally, without being constrained by preconceived notions arising from the senses.”

If there really is wisdom, it tends not to make a fuss of itself.