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)
Continuity mistake: When the song about Ebeneezer Scrooge is about to end, just as Ebeneezer is walking down the last lane, the first Muppet you'll see to the left when he has come down the stairs is wearing a red weird hat. Just a second after Scrooge has walked past the lady with the funny hat, when they sing, "If being mean's a way of life you practice and rehearse," you see the same Muppet with the same hat, now standing in front of Scrooge. She had no time to get there between the two shots.