What Lego set has the most unique colours?
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.