At what stage is it wrong to consider oneself wise? Is it always wrong to consider oneself wise? 

I don't mean consider oneself an important Buddhist, or one who has attained such and such a level of absorption or success along the path to enlightenment, but 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.
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.