On top of the troubles of either giving him actually wise things to say, or convincing us that he's wise by rhetoric without actually committing yourself -- there's the question of point of view.
I've recently been reading a book where there is indeed a wise character -- grave, foresightful, prudent -- and then in one scene he went to explain himself to another character.
Not throw against the wall bad, but it struck a false note. Rather like the few stories where Doyle made Sherlock Holmes the point of view character, or the one where Wodehouse made Jeeves. It is very, very, very difficult to actually tell a story from the impressive point-of-view.
Even the mere verbal side of it is quite hard enough. I have been known to observe that many fictional sages would be improved by ripping off Marcus Aurelius's Meditations, but then I recently re-read and was pondering, philosophically, how much my understanding was predicated on my previous knowledge of Stoicism. It's not easy, figuring out what sort of wisdom to put in their mouths.