Factual error: During the opening credits, the show's copyright date is shown in Roman numerals as MCLXIV. In Arabic numbers, that's 1164 - it should have been MCMLXIV for 1964.
Other mistake: At the end of the show when the misfit toys are being delivered, the elf in Santa's sleigh gives an umbrella to each of the misfits so they can glide down with the exception of the bird, who jumps off, apparently forgetting that he is a misfit toy and can't fly; as he stated earlier in the show, he can only swim.
Revealing mistake: Whenever Rudolph is walking you can see the tracks he makes before he even puts his feet down.
Continuity mistake: When Rudolph and Hermey sing the Misfit song and they are crossing the wood log across the crack, at first the shot is under Hermey and it shows Hermey crossing half of the log. When the shot comes above Hermey, he is once again where he started.
Audio problem: At the end of the elf concert, when Mrs. Claus walks right out right after Santa does, we hear the sound effect of a door slam before she even closes the door.
Other mistake: Right before the snowman starts singing "Silver and Gold", a seal hands him a banjo. However, when you hear the song playing, there are no banjo sounds in any of the music.