I just got my iPad back from a guy that swapped its cracked screen. I was happy to get my favorite toy back so I loaded fresh 6.0.1 firmware and it and everything was OK before I noticed really crazy things.
Take a look on this video: (the forum rules do not allow to post links for newbies so I am forced to remove it but I can send it to you if it will help to identify the problem)
Sometimes, my iPad goes into weirdo mode and starts doing crazy things. It moves, resizes or closes browser pages. It opens apps. It uncontrollably schools through the web pages or opens task manager bottom tray.
Have you seen something like that? Can that be related to something that was done during screen replacement?