In the episode 'Apocalypse', Eddie (disguised as the grim reaper) states that he doesn't know how to play chess, and Richie says that he will teach him. However, in the later episode 'Culture', it is the other way around - Eddie knows how to play chess, and Richie does not.
In the episode where Richie and Eddie look after the shop, Richie is doing a rain dance with his trousers pulled up over his knees. One of the trouser legs falls down but in the next shot it is up again.
When Richie falls down the stairs in the Carnival episode while impersonating Kilroy, he rolls into the bathroom and gets stuck in the toilet head first with his feet in the air, however just after he falls through the door before the camera moves in you can see his foot protruding from the doorway