When Ethan pulls Hallie away from Santa, her fur muff disappears as they are running away and then reappears as they are talking.
Snowball, the mouse, is sometimes a boy but is mostly a girl.
When Ethan calls for a tow truck to remove Tony's car from in front of the diner, he says it was abandoned several days ago. But when the tow truck arrives, the lights are on and the engine is running.
When the kids go to the pet shop, Ethan only puts three mice in the box, but the clerk counts it as eight and they later have eight mice when they're being released.
As the kids return to Lillian's townhouse on Christmas morning, there is a building around the corner from where they're walking. It is not present in the matte painting shown throughout the film and instead a bridge is shown to be around said corner.
Ethan falls asleep while playing a home video of his parents, obviously on videotape, since it is 1991. When he wakes up in the morning, the TV is still showing a freeze-frame of his parents kissing. A video cassette would have shut off within a few minutes of freezing and would display only a blank screen or, if tuned to a broadcast, to a program.