When Alice places bacon on George's plate, she puts down two. Before Beethoven eats one, there are three. This is because the same footage of bacon being placed a plate was used twice (which had two pieces).
In the scene after Beethoven "attacks" the vet, Dad goes into the backyard and gets Beethoven to take him to the vet's office, the dog's neck and snout are mysteriously clean even though only moments earlier they were smeared with fake blood.
When Ted and Rice are playing Super Mario Brothers 3, they are both mashing away on controllers, however, when it shows the close up of the screen, we see that they're only playing a one-player game at the time.