The ticket booth operator lists a bunch of locations that would be counterintuitive to travel to (Saskatchewan is in central Canada, Hudson Bay eastern Canada, Nome is in FAR western Alaska, a whole trip across the continent westward, the Klondike is in the Yukon, a southwest backtrack) until you realize he was humoring the kids and trying to say that there's no way to travel by train to the north pole, which is a bunch of ice floating in the Arctic ocean. There isn't even a land bridge between Canada's Ellesmere Island and Greenland. Had the kids had the $3000 for the ticket, he would have had to admit he was making stuff up or make up a story about train service not being in for one of the lengths of the journey.
Many remember the scene where Professor Hinkle is told by Santa that he has to write an apology "a hundred zillion times" to receive any goods, but the dialogue originally began as a threat that if he touches the hat he'll never receive another Christmas present again. Hinkle then names examples of things he would want. If there was continuity to the discussion, after he said that he had to make a living too, Santa would have said something like "Well you'd better not touch that hat, then".
In Rudolph and Frosty's Christmas in July, Frosty and Crystal have children! Um...how do snow people procreate? Did they make them and bring them to life? Magic? Um...
Why does Frosty always say "Happy Birthday" when he gains consciousness? Whose birthday does he think it is? He can't be referring to himself, you don't say "happy birthday" when it's your own birthday!