Other mistake: In this movie, Gandalf looks older than he does in his grey incarnation in Lord Of The Rings: The Fellowship Of The Ring. However, this takes place before the Lord Of The Rings trilogy, so he should look younger, or the same.
Other mistake: When giving Sting to Bilbo, Gandalf tells him it is an Elven blade and will therefore glow blue when Orcs are near. However, Glamdring and Orcrist are also stated to be Elven blades, but they do not glow blue.
Other mistake: Just after he arrives at the gathering Thorin states that he wouldn't have found Bag End had it not been for the mark Gandalf made on the door. Bilbo then claims that 'There is no mark on that door, it was painted a week ago'. However in the earlier scene where Gandalf makes the mark the paint work is cracked and weathered, more than it would have done after only a week.
Other mistake: When an invisible Bilbo is about to jump over Gollum to exit the cave, you can see Gollum prepare himself for impact just before Bilbo jumps over him. This isn't logical if Bilbo is invisible.
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