Homer enters Scorpio's lair to get some sugar. Homer is holding his mug when he enters. When Scorpio asks Homer what his least favorite country is, Homer's mug has vanished and his hands are at his sides. In the next shot, Homer is holding the mug again and it is visible for the rest of the scene.
When Bart realizes that the remedial class is going slower than the other kids when they're supposed to be catching up to them, Bart says, "Cuckoo." The other kids in the class then catch onto Bart by repeatedly saying, "Cuckoo." However, one of the boys, Gordy, is not making the "Cuckoo" sign when he starts, but in the next shot, he is. He is not seen raising his arm to make the sign.
The Simpsons move away to Cypress Creek and abandon their old house, yet only take one car with them (the station wagon), while the other just disappears and is never seen until the next episode.
Lisa does not appear to attend Cypress Creek Elementary, or skips classes, because any time Bart is seen in the school or the Leg-Up Program, Lisa is out in the forest. However, if any of the Simpsons were going to skip school, it would be Bart, not Lisa. This is an unintentional mistake as the reason for her being in the forest is to provide an additional reason why the family wants to leave Cypress Creek. The reason Lisa wants to leave is because she is allergic to everything in Cypress Creek.