Hey guys, having the same problem here. Home button has become wonky over the past 1-2 weeks, occasionally registering single clicks as double clicks, and vice versa. Has been happening more frequently as of late, about 6-8 times in the past hour.
Called up AppleCare and they redirected me to my mobile service provider, since we don't have an Apple Store locally. I've yet to make an appointment though. I've tried blowing the dock connector port and using a small brush to sweep out any dirt inside, but it hasn't really helped.
One question though: if I exchange my iPhone for a new one, and I resync my new iPhone with my computer, I know I'll restore all my apps and messages and the like, but will I retain all my in-app save games? Have spent ages completing Angry Birds and to lose all that data would be a bummer! Sadly, that's what's keeping me from trading my phone in, haha.
On a 32GB iPhone 4, non-jailbroken, purchased August 2010, if that helps!
Yes, everything you restore will be there when you revert your new iPhone to your backup file.