Clearly, Rickman has more emotions to mine in this movie, and he does it well, so I'm sticking with my prediction.

Or we could give the Oscar to Warwick Davis for his double duty as Flitwick and Griphook. (Poor Verne Troyer.)

I probably napped through a key moment but how did Droopy Horseface end up with the sword?

Not the Larry King goblin, the horse-faced kid at the end.

He pulled it out of a hat.

That hat he found in the rubble? I'd thought that was the damaged remains of the sorting hat. What was its significance and why was the sword in it (I assume the hat was like Hermione's purse and large on the inside)?

I assumed it was some detail from the book that they left out. Haven't read them. It looked like the sorting hat to me too, but I wasn't sure because it didn't talk.

I think it's the same hat the Phoenix came out of in an earlier book/movie.

I can't quite recall and I did read the books.

I could be completely wrong, but doesn't the hat produce whatever the person reaching in needs the most at that moment?

ETA: Looked it up. The sword (which was Godric Gryffindor's Sword) "was said to appear whenever a 'true Gryffindor' was in need." And yes, it appeared for Harry from inside the sorting hat in Chamber of Secrets.

Deus ex machina: It's not a bug, it's a feature.