Revealing mistake: I'm not sure of the episode, but it is somewhere in Season 7. The family was having dinner while Nicky and Alex were upstairs. When the Tanners were having ice cream sundaes, Jesse decides to bring some upstairs to Nicky and Alex. When he sets them on the table upstairs, you could see that they are props.
Continuity mistake: Jesse is playing Hide and Seek with Nicky and Alex. One twin is wearing blue pants and the other is wearing green. After Jesse says, "Go hide!" the first time, he tickles the twin wearing blue pants. This twin runs into the hallway, but the hallway shot shows a boy wearing green. Cut back to the bedroom, and the twin in the room with Jesse is wearing green pants.