If you ever run into the problem where your iPhone thinks that you have an invalid password for Gmail (although you know you’ve typed it in correctly), then from your Safari browser in your iPhone do this:

https://www.google.com/accounts/DisplayUnlockCaptcha

I found the fix here:

http://www.google.com/support/forum/p/Google+Mobile/thread?tid=7aa4c4e9ffd8a5f9&hl=en

Hope that helps somebody!