I had another whinge to Apple Support last night because I want my ipad to be replaced before the warranty runs out. I would feel better knowing that its more likely to be software if I do get it replaced.
Unfortunately, Apple want me to continue with it to determine if it is software or hardware and won't just swap it going by what I've experienced. I was asked to backup everything and factory reset it (erase all from Settings), and set it up as a new device (to rule out any corruption or restore issues). I've done that, and I was looking forward to a fresh start and installing and setting everything up again.
This morning, I've managed to get to a point where I can reproduce some home button weirdness! I was setting up mail from within Settings (Exchange to Gmail via m.google.com), and it all went through until I got to a dark blue dialog window asking for my account password (which should be my Google app specific password). I hit the home button so that I could use Safari to set that up, but the home button wouldn't work again. It could double click, but not single click. I cancelled the password box, and I could single click again! I went in to the Mail app and it happened again when it asked for the password.
Not quite what usually happens, but definitely a software issue there. If anyone has the time to try the mail password thing to see if the same happens on another iPad, we might be able to at least highlight a bug that's related...