Continuity mistake: When Papa is showing Buddy the sled at the beginning of the film we see the Clausometer (the middle odometer)and the indicator is pointing to the left at around 15 (9pm position). As Papa gets in the indicator is now pointing at around 35-40 (10pm position). Later in the scene when it show a closeup of the meter it is back to 15 and then the last shot of it its 35-40 on the meter. The changes are instantaneous between shots and there is not enough time for them to move that much.
Continuity mistake: After baby Buddy crawls out of Santa's bag at the North Pole workshop, he is partially sitting on the edge of the bag, grasping the leg of a teddy bear. The next shot and the baby is over a foot from the bag, and not holding on to the bear's leg, which is still in the bag.
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.