The train on the Island of Misfit Toys is there because his caboose has square wheels. At the end of the show, however, when the elf is dropping toys from Santa's sleigh, the train no longer has its caboose.
When Rudolph, Hermey, and Cornelius are floating on the ice, we can see the dogs lying on the sled. When it crashes into the Island of Misfit Toys, the dogs are gone. Obviously, they reappear later in the movie, just before Hermey and Cornelius arrive at the Abominable Snowmonster's cave.
During the scene leading up to Santa's plea to Rudolph to guide the sleigh, Rudolph's nose keeps changing its size and shape.
Rudolph's throat and chest markings change drastically in the last third of the film.
The jingle bell garland that Santa gives Donner doesn't appear until seconds before "Jingle, Jingle, Jingle" begins.
The opening credits are in all capital letters. At one point Burl Ives' name is spelled BURL IVES but later it's BURI IVES. This was corrected in the 50th anniversary collector's edition blu ray/DVD combo.
The female reindeer have no antlers. These are the only deer where the females also have antlers.
While Mrs. Claus is telling Santa to eat, the food shown is gray and unpainted.
When Hermey is making "oink" sounds to lure the Bumble outside the cave, it appears at one point that he doesn't have a mouth.
At the beginning when Rudolph is born, Donner says "How can you overlook that?" As he does, his antlers bend dramatically, but rise back up when he looks at Santa arriving.
When Clarice and Mrs. Donner leave the cave to search for Rudolph, their shadows disappear as soon as they are out of the cave, indicating that they were removed as soon as they were out of range.
As Rudolph and Santa are about to land on the Island of Misfit Toys, the fire that the toys are sitting around is gone even though the glow surrounding the firewood can still be seen.
Although the film was copyrighted and released in 1964, the Roman numerals copyright date in the main titles is shown as "MCLXIV," which would be the year 1164, eight centuries earlier. 1964 is MCMLXIV, in Roman numerals.
During "Silver and Gold," Sam the Snowman is handed a banjo and begins plucking it. However, no banjo is heard in the song.
As Sam introduces the Christmas seals, clapping is heard in the soundtrack, but none of the seals is clapping.
When Mrs. Claus goes out the door after Santa, the sound of the door slamming occurs before the door is shut.
After Hermey pulls all of the Abominable's teeth, he tells everybody in the cave "Don't let this big blowhard scare you anymore, just walk right past him." It is clear to see that he is not talking. In fact, he doesn't even have a mouth.
The head elf's voice is clearly a different actor when he's conducting the choir.
The Abominable Snowmonster's legs are longer when they first appear than they are on the actual doll; these legs are actually those of an animator.
When Rudolph, Hermey, and Yukon Cornelius are inside their cabin on the Island of Misfit Toys, in spite of the Arctic deep freeze, flowers can be seen blooming in all the window boxes.
When Santa leaves at the end, with Rudolph at the head of the team, there are only seven reindeer altogether (including Rudolph himself). There should be nine. The reindeer were divided in a subplot which was cut from the final film.
When Rudolph returns to Christmas Town Santa reveals that his parents are gone, looking for him, and there are two days before Christmas Eve. Santa further adds that he can't get the sleigh off the ground without his father, Donner. But at the end when Santa's sleigh takes off with Rudolph taking the lead, Donner is on the ground, watching as they leave.
The rationale for Rudolph leading the sleigh is foggy weather, yet when the sleigh takes off and throughout the subsequent delivery, the weather is perfectly clear.
Sam the Snowman said that when Hermey and Yukon arrive in Christmas Town just as the storm hits, he himself sent them to the cave of the Abominable Snow Monster. But how did Sam know that Rudolph and the other reindeer were in the cave?
During the fight with the Bumble in his cave, all of the reindeer seem to forget that they can fly, and don't attempt to use that capability tactically.
When the elf is dropping presents from the back of Santa's flying sleigh at the end of the movie, each toy is handed an umbrella for them to use as a parachute. When the elf comes across a toy bird, he pauses and then tosses the bird over without an umbrella, thinking it wouldn't be needed. Unfortunately, that particular bird was the one from the Island of Misfit Toys, and cannot fly (but swims).
Donner and Comet's voices are identical. The actor voicing the characters apparently made no effort to do different sounding voices for the characters.
The elf "Hermey" is called "Herbie" by some characters.
When Rudolph leaves Cornelius and Hermey in the cabin to set out on his own, the narrator says that Rudolph does this as to not "endanger his friends lives any more." Yet, when he exits the cabin, he leaves the door wide open in supposedly frigid North Pole temperatures.
When Rudolph is in front of King Moonracer he states "When and if we ever get back [to Christmas town] we'll tell Santa." This is in response to Moonracer asking them to get Santa to distribute all the misfit toys. "Dolly for Sue" in response to Charlie-in-the-Box's comment about having to wait another year says "But Rudolph promised we'd go this time." Rudolph never made such a promise.