Continuity mistake: In the scene where Tony has a bloody nose his mom has put tissues in it to stop the bleeding. She pulls out one side and says still bleeding so she gets more tissue, while she is rolling it up there is no tissue in that one side of his nose. Then after she is done rolling it up the tissue is back in his nose without her putting it there, then she pulls it out again and replaces it with fresh tissue.
Visible crew/equipment: Sometimes, especially at night, you can see the lights of the equipment reflect off of Tony's glasses. We know this isn't the moon or a car light because for one thing it's the wrong shape and when Rudolf is sucking blood out of the cow there is no moon or car nearby. So there is only one place the light could have come from, and that would be the crew equipment.
Continuity mistake: When Tony puts Rudolph into the chest at the end of his bed, he climbs into bed with his red tee-shirt on. In the next shot, his red tee-shirt is neatly folded up, and is sitting on the chest, and Tony has now got a pajama top on.
Continuity mistake: Right before Anna comes into Tony's bedroom (when she teaches him to whistle), Tony is sitting on his bed wearing a sweatshirt and jeans. When Tony hears the approaching footsteps he dives under the covers, and he is wearing his nightshirt.
Continuity mistake: In the scene where Tony first meets Rudolph. Tony has his fake vampire teeth in and is pretending to bite his teddy-bear. He uses tomato sauce to simulate blood and has it all over his face. He uses his left sleeve to wipe his face completely clean, yet for the rest of the scene the tomato sauce keeps appearing and disappearing and changing shape.