Revealing mistake: When there is a flashback of Thorin in the war, in the first few seconds, on the left of the screen, there is a man with a shield. He swings it at an ogre and you can see it misses by a good five inches, but the ogre moves his head back as if it were hit.
Revealing mistake: When Gandalf marks Bilbo's door, you just see the outline already marked on the door. (01:15:10)
Answer: Hobbiton is the village where Bilbo was born. Overhill is on the northern edge of Hobbiton and Underhill is at the bottom of said hill. Built into the hill itself is Bag End, the Baggins estate. The Shire is the name of the Hobbit lands overall. So, he's from the village of Hobbiton in The Shire, and his home is Bag End, which is in the midst of the hill that forms both Overhill and Underhill.
Captain Defenestrator