Deliberate mistake: Jesse is looking for his keys and thinks Michelle took them. Near the end, Joey comes home and finds the keys in the door, hands them to Jesse, who puts them in his pocket. A few seconds later Danny comes home, takes Michelle into the kitchen. Joey and Jesse exchange a couple lines and go into the kitchen, where Michelle is sitting in a booster chair at the table. The 3 guys chat for a few minutes, then Jesse is going to leave, but can't find his keys again. It turns out Michelle has them. But how did Michelle get them? She was in the booster seat the entire time Jesse was in the kitchen and Jesse never went to that end of the room, so there's no way she could have gotten them.
Continuity mistake: When Danny is sleeping, Stephanie wants to dance her dance. She goes and gets her tape. When she starts to dance, we can hear it's a tape (because it's the real singer who is singing), but when she is finished, it's the band who is playing the song.