One problem I am having with my iPhone 4, gmail, and IOS 6 is that I receive an e-mail alert when the icon badge goes up a number or goes down a number.
All I did was upgrade to IOS 6, and this false e-mail alert started happening. Very annoying since the iPhone does not always update immediately after I check my e-mail on a PC. 5 minutes later, my phone is vibrating and no new messages! Just alerting me that I now have less messages than before...