Recall that in the Chamber Of Secrets, the sword was 'pulled out of the hat' by Harry Potter. The Hat and the Sword have some odd relationship in the books thats never explained. Somehow, the hat has the ability to deliver forth the sword.

Yes, the goblin 'stole' the sword, but I think the point is that the Hat can always produce it. Some sort of 'portkey' for the sword.

I can't recall how the hat made its way to the the battlefield, or why Neville would have thought to drag it along. Yeah, I know... The Yeti Reads Harry potter... ;-)

Now- the REAL screw up of the entire series was the mirror given harry by serious in the Order of the Phoenix. This Mirror was supposed to allow instantaneous 2-way communication between Sirius and Harry. Yet, the entire plot and even ending of the Order of the Phoenix was driven by Harrys inability to communicate freely with Sirius Black. Even after the characters did back-flips to finally 'get in touch', Sirius never said: 'Hey, you stupid brat, use the mirror!'. Only after the eventual death of Sirius, caused by the aforementioned inability to reliably communicate, does harry 'remember' the mirror. And then no mention is made by how it would have obviated the entire plot.

Furthermore, while the mirror played a minor role in the last book, it was entirely unecessary to any aspect of the story. That pretty much ruined the 5th book for me, and almost caused me to stop reading the series.