Continuity mistake: In the first film, it is mentioned several times that Kevin is 8 years old. However, in this film it is stated that he is 10. When his parents are in the Miami airport security office, they say that he was left alone last Christmas. That would make him 9. Both films take place the same days, from about three days before Christmas until Christmas morning, so even if Kevin is born around Christmas time this is still a mistake.
Continuity mistake: Just before Batman takes his mask off at the end, the black makeup around his eyes vanishes while the mask is still on. (01:48:20)
Revealing mistake: During the ghost of Christmas present, Kermit is walking with tiny Tim on his shoulder and you can tell Kermit is walking on a spinning drum. Right before the camera pans away you can see Kermit's feet slide like he stopped walking but the road kept spinning. (00:55:00)