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.
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. (00:13:40)
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.