Continuity mistake: When Buddy's dad opens the present from Buddy, he holds it directly above the box. In the next shot, a closer shot, he is holding it next to the box. The following shot shows him holding the present directly above the box again.
Continuity mistake: When Buddy is on the ice floe beginning his journey to New York City, Mr. Narwhal emerges from the water. Buddy's body is canted back with his left arm raised as he watches Mr. Narwhal surface, but the next shot of him shows him standing straight with his arms by his side.
Other mistake: When Buddy confronts the department store Santa (Artie Lange), watch the kid sitting on his lap. He's mouthing the words of both Buddy and Santa as they're saying them.
Continuity mistake: When Buddy is in the Lincoln tunnel, the busses alongside him change positions between clips.
Other mistake: When Buddy's brother gets a skateboard from Santa Claus in Central Park the skateboard trucks are mounted incorrectly. Both are mounted the same direction. The kingpin always faces the inside of the board, but here one is mounted facing outside.
Continuity mistake: When Buddy is drinking the Coke, the bottle turns to show the label.
Answer: It might just be a regular elf doll that, coincidentally, is dressed in real elf clothes.