This is driving me nuts because I had the hero and swapped it out to the Moment and it did the same thing. I am using the Gmail app and whenever I get new mail I have to go into the ALL MAIL label to see it even though the mail has a Inbox tag on it. By doing this I don't get any notifications of new mail and must check it manually. I've tried clearing out Gmail app and Gmail storage but it will only sync once and stop again. So anyone having the same problem? Gmail not pushing mail into the inbox? I posted on google help forums but so far people only told me to clear data of the applications.
Its only happening in the Gmail App on the phone. The Gmail Web does indeed transfer the mail correctly.
I think i found a possible solution to this, so if you created a gmail account on the phone itself when you first booted it up it doesn't sync correctly. I went ahead and created a new gmail account via web. And now everything gets pushed to the inbox, and i don't have that problem of SENDING stuck in the outbox also. So go in disable gmail sync then clear the data from Gmail app, Gmail Storage, and Google.app. Insert your new gmail account when you turn sync back on and it should work.