Continuity mistake: When Buddy first meets Jovie, she is wearing much more make-up by the end of the scene. The amount of lipstick increases quite a bit, for example.
Continuity mistake: When Buddy is lying in the roll-out bed in the living room of his father's house and asks to be tucked in, his father does so. His father comes back up and ends up having a red thread on his shirt. The shot switches to Buddy, then back to him and the thread is now on his right arm.
Continuity mistake: In the snowball fight scene we see some snowballs hit the rock behind them. The snow on the rocks keeps disappearing and reappearing between shots.
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 in the Lincoln tunnel, the busses alongside him change positions between clips.
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.