My personal email is handled by Google Apps with me using OS X Mail.app at home via IMAP, web-based access from work and push (Exchange) access from my iPhone 3GS. All in all a nice combination except for a few niggles of ghost items in my iPhone inbox.
Quite often my iPhone will show items in the inbox that are not visible from the web interface or via IMAP. These messages were in my inbox for a bit but eventually deleted (where they can be found in the trash). It seems to only occur when deleting a message from Mail.app via IMAP. Of course it would be too simple if this were consistent as it's going through phases of doing it.
Looking at the ghost items in the trash (via web view) shows that they still have the 'Inbox' label applied. But that's apparently fine as other deleted items that are not ghosting seem to have that as well.
So all I can figure out is that it must be a gremlin on the Google side when a delete occurs via IMAP. I'm guessing Mail.app is not at fault as the item does move to the trash but there must be some odd state that the Exchange support is picking up on to show those items.
Here are some screenshots of the iPhone inbox and web view. And since I'm on the free version of Google Apps I don't get support so have no clue how to report this to Google.