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.
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.