What Lego set has the most unique colours? What Lego set, past or current has had the most unique colours (colors) regardless of piece count? 

I've found bricklink's color list but I have not found any way to filter sets biased on most colors.
I have no idea where to find any sources for an answer, but I can offer a guess.

When it came out 70620 Ninjago City was the set with the most different elements ever made (That wasn't hard to verify, if I can remember how, I'll check later if it still is, and if any other contenders offer more colours), a guess is that they will come in many different colours. And they do, if I counted correctly there's 51 different colours in that set, quite a bit more than the 20 @Joubarc mentioned in a comment.