Fans of "Married With Children" know that every tenth episode or so, Kelly the dumb blond is "caught out of character" for a second, discussing nuclear physics or something on the phone, before "discovering" the camera and resuming her airhead persona.
My Dad used to do that from time to time. He's say something so funny or intelligent (HUGELY out of character) that I'd spend the rest of the day trying to figure out whether he'd said that on purpose. I can't seem to recall any specific examples though.
When I was helping a friend move into an apartment, he was attempting to sink a nail into the wall, to hang a shelf. After several attempts, he shouted out "Damn! I cannot find a stud to save my life!" Our other friend and I immediately started vamping it up behind his back, but he never turned around. Interestingly, now those same guys occasionally call to borrow my electronic stud-finder.