When Rudolph is getting ready to run away from home, you see the back of his head when he's looking at the picture on the wall and there is no blonde hair at the back of his head. However whenever you see the back his head in other scenes, he has got blonde hair.
When Rudolph gets disqualified from the reindeer games, the referee clearly removes the winners' wreath from around Rudolph's neck to give to Arrow instead. However in the next scene, Rudolph is seen with the wreath still around his neck in the background and his rider is taking it off him.
It continually changes between day and night between the scenes of Rudolph's disqualification and when Santa lets him draw his Sleigh.
Penguins like Stormella's Butler Ridley are not native to the North Pole, or anywhere in the Northern Hemisphere.
Reindeer are the only species of deer where both genders have antlers, but in this film, only the Male Reindeer have antlers.
While trying to find a way out of Stormella's Castle, they never think to follow Rudolph and Leonard's footprints, which is what they saw when realizing that they were going round in circles.
In the Reindeer games race, Rudolph was #5, Zoey was #7, and Arrow was #1. When Arrow ticked off Rudolph causing his nose to blind Arrow and caused the crash that took a lot of the field out as a result, Zoey made it through and came in second. If you watch it, it was #5 and #7 that crossed the finish line in that order. So technically, when Rudolph lost the race by a technical fault, Zoey should have been declared the winner by default.
How was Rudolph able to write a note and pack his backpack upon running away with hooves.
Some of the speech was out of sync with the visual.
Slyly never explained how he was able to get into Stormella's Castle undetected, and why he decided to eventually come in.
How the Avalanche that forced Slyly and Rudolph out of Slyly's cave is unknown. Same said as to what happened to the Female Foxes.
It's not known why Arrow's cheating by knocking others out of the race wasn't noted by anyone.