Revealing: Whenever Rudolph is walking you can see the tracks he makes before he even puts his feet down.
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: 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.