Currently there are some problems with google mail accounts on iPhone 3.0.
Functionality as designed should be that when you move a message from the Inbox on the built in mail application it will move it to the correct folder and remove it from the inbox. I often use this to archive mail to [Gmail]/All Mail folder.
When you move something from the inbox at the moment it does the label part but doesnt move it out of the inbox. So when you check youre email on the web, or another client, the mail is still in the inbox. My set-up was working fine on 2.2.
Today I've tryed turning mobile me off, google spanning sync, installing my Gmail Account using the iphone wizzard, manually adding a IMAP account and finally adding Google Exchange support. No changes anywhere. My friend also has the same issue. Not sure if its a Google or Apple problem.