Blooper: Santa's sleigh is supposed to have eight reindeer pulling it (Dasher, Dancer, etc.), which would make 9 total when Rudolph is with them. But when we see the sleigh being pulled at the end, including Rudolph, there are only seven.
Channel Hop: The 1964 special went through a couple of networks over the years. NBC held the broadcast rights to the special until 1972, when CBS snapped up the rights, and it has remained on the network since then. However, with the acquisition of DreamWorks Classics (the special's current rightsholder and main licensee of the Rudolph character) by NBC's parent company, NBCUniversal, in 2016, the special could return to NBC once again when CBS's rights expire.
Cross-Dressing Voices: The titular character was voiced by Billie Mae Richards, who was ironically credited as Billy Richards from 1965 onward, as mentioned in obituaries mourning her death in September 2010.
Keep Circulating the Tapes: The 1998 film and its sequel have been long out of print, both on VHS and DVD, with no plans for re-release for either. The sequel aired on ABC Family for a time until their rights lapsed in 2013. DreamWorks Classics is believed to own both films (as with the 1964 TV special), but they've been sitting on both ever since.