Visible crew/equipment: In the scene where Buddy and Michael are leaving the school, a crew member is visible in the bottom left of the shot. At first, he is just standing there, but he then tries to hide inside a doorway. (00:52:00)
Visible crew/equipment: Widescreen only. When Buddy is chasing down Michael after school, just before the camera cuts if you look at the far left of the screen you can just see a boom mic entering the shot.
Visible crew/equipment: In the scene in Central Park when Santa's sleigh has crashed and Buddy is repairing the engine, the line that is holding the reindeer in place is visible on the lead reindeer. Not the harnesses that are around each reindeer but the line that is keeping the lead reindeer leashed to the ground is visible.
Visible crew/equipment: Before Buddy goes to New York, he is talking to the snowman, and while he is walking with him, you can see multiple shadows. One to his left, right, front, and back at least.
Visible crew/equipment: When Buddy fudges with the fake Santa and the mall is destroyed you get a glimpse of the lighting set up and a crew member in the top left of the screen.
Answer: It might just be a regular elf doll that, coincidentally, is dressed in real elf clothes.