First of all, calm down like seriously. It's a children's movie, you seem to be taking it a bit too personally. There are virtually no movies aimed at children without plotholes. They aren't meant to be sophisticated.

Jamie is the "last kid that still believes on earth"

Maybe his sister was too young to really separate reality from fantasy. It seems like the choice to believe is what is important, and since younger children are naturally naive they will believe no matter what. As an older kid you face the reality of the world, and you can either listen to those around you or stay strong in your convictions.

The entire world stopping believing in the toothfairy because she missed ONE night collecting teeth?

Yes. Are you ever around children? We're also assuming it was just one night. Time isn't really presented in the forefront in movies aimed at kids. It's cold outside with snow then it's suddenly Easter? The details just aren't there because kids aren't going to question it. Remember that is their target audience, not you.

Then why leave out Halloween from the roster?

Because it's based on a series of books. There isn't a Halloween Guardian, at least not one that has been presented. These books are ongoing, and the author is working on one focusing on Jack.

Why have the EXACT parallel of Jack curing the child Bully of her meanness?

Because regardless of her personality she is still a child. Comparing a troubled child to a malevolent spirit is asinine. Read the books, then you'll get a better grasp of who Pitch is. It's obvious you really infatuated with his character, but giving him an ultimate redemption when it doesn't happen in the books makes absolutely no sense. That's like Voldemort's life being spared because I liked his character. Not to mention he went toe to toe with Jack and held his own. Do you really think a simple snowball was going to be enough to turn him? That's just plain stupid.