Dan's Boss - S3-E7
Corrected entry: Approximately seven and a half minutes into the episode, Dan's new boss, Vincent, corrects Christine on a precedent she cited, then says it was overturned "On August 17, 1977. I believe it was a Thursday." Harry jokes, "It was a Tuesday." According to The World Almanac and Book of Facts, it was actually a Wednesday.
Undressed For Success - S9-E14
Corrected entry: In this episode, Harry is putting together an unpainted plastic model of Frankenstein's monster. In the previous episode, 'A New York Story,' the model is put together and he's almost finished painting it.
Correction: That's because the episodes were aired out of order and not a mistake in the show. Episode 14 (production code 18741) was produced before episode 13 (production code 18744).
Correction: It's entirely possible that he was just mistaken, not necessarily a mistake on the researchers' behalf. Also, as you've pointed out, Harry was making a joke...