The Onion A.V. Club has a fun article about bad scenes in great movies and great scenes in bad movies. The picks for the former are mostly spot-on, while I haven't seen enough of the latter bunch of movies to comment (except Walk on the Wild Side, the most famous example of a movie where the title sequence outshines the actual film).
I should add my own choices for worst scenes in great movies, but I need to think a bit more about it. I could pick scenes that I think are just overrated -- like the hunting scene in The Rules of the Game, an overlong bit of heavy-handed preachery that drags down an otherwise subtle movie with its five-and-ten-cent-store symbolism -- but for the most part, even the lesser scenes in good movies tend not to be bad. That's why something like the psychiatrist scene in Psycho, a scene that is not only heavy-handed but cheesy, clumsily shot, and generally badly done, is a gift from the Gods: a scene in a good movie that seems to have wandered in from a genuinely bad movie. I need to think of a few more scenes like that.
One filmmaker who does come to mind as perfect for something like this is Blake Edwards. He's never made a good movie without some really atrocious scenes, and on the other hand even his worst movies have some pretty good things in them (Curse of the Pink Panther is almost -- almost worth it for that closing gag with Roger Moore). If I liked Breakfast at Tiffany's enough to consider it a great movie, any scene with Mickey Rooney would be an easy choice for the "worst scenes in great movies" list.