Q: Mavericks Mail App and Gmail folders

Yes, this is a known issue.

If you show "all mail" in Mail then the messages will transfer properly.  But if it's not hidden, it doesn't appear labels are properly applied and thus the "inbox" label is never removed from the messages.

Yes.

This is one of the largest bugs in Mavericks’ Mail app, which affects Gmail accounts and Google Apps email accounts. This used to work just fine in previous versions of OS X, so it is a brand new problem in Mavericks:

Mail can’t delete messages from the Inbox unless Google’s “All Mail” folder is visible in Apple Mail. If you try to delete a message from the inbox, the message only disappears temporarily, then reappears moments later. It seems like Apple Mail never removes the “Inbox” label from the deleted messages, so the messages just keep reappearing back in the Inbox over & over again.

The workaround is not a desirable one: It requires the user to make Google's “All Mail” folder visible to IMAP clients (via Gmail's "Settings>Labels” page). However, this workaround is not desirable because of 2 bigger problems:

(1) Making the “All Mail” folder visible in Apple Mail will suddenly make dozens of gigabytes of emails start taking up valuable hard drive space, because every single email that has ever been archived on Gmail/Google Apps will suddenly be written to the Mac’s hard drive. This can be a real problem on a machine with a small hard drive, such as the MacBook Air. Hiding the “All Mail” folder prevents these messages from taking up valuable hard drive space.  Not to mention that all of these messages are DUPLICATES OF MESSAGES THAT ALREADY APPEAR in other IMAP folders, so showing the "All Mail" folder in Mail is absolutely pointless.

(2) Whenever the “All Mail” folder is visible, every new message that comes into the “inbox" also shows up as a new message in the “All Mail” folder as well, so new messages appear like they are coming in twice. Also, users are forced to mark their messages as “read" in two locations: the “Inbox" AND the “All Mail” folder.

The ideal solution would be for Mail to operate how it used to operate: Users should be able to delete messages from the Inbox, without having the “All Mail” folder visible in Apple Mail.

Please report this bug to Apple at http://www.apple.com/feedback and hopefully they will fix it in a software update soon!

I'm running Gmail IMAP here w/out All Mail visible to Mail.app and am able to delete email without issue.

However, I did have a problem with an incorrect mail count showing next to a Smart Mailbox in the side bar. I followed the instructions by Hackintosh (7th post this page: https://discussions.apple.com/thread/3780528?start=0&tstart=0) and that was cured.

Could be I had the same Gmail IMAP problem as you but cured it without knowing I had the problem.

Apparently if you endure through downloading copies of All Mail to your Mac, after the download you will only have one copy of each email, not multiple copies like in the previous version. More info here: http://tidbits.com/article/14219

Same problem for me, though it seems to work fine for my normal gmail account, but not my apps for domains account. Weird.

Due to this article problem #1 isn't a problem because messages don't take double space in Maverics. They stored only in All mail folder physically and in others folders just logically.

Problem #2 for me isn't a problem. There's no need to look into the archive and reed letters. No matter how many unread letters it shows.

But, in the same article another greater problem was described - mail.app periodically renew information about labels and don't receive new emails during the procedure (several hours). That is very sad, but it can be fixed in newer updates.

I, too, am having this problem with a gmail account from Google Apps.  I filed a bug ticket this morning with Apple.  Hopefully a fix can come soon because this is terribly disruptive.  For the time being I'm using my iPad to file mail from my gmail account as the Mail client in iOS works just fine.

Scott Rose wrote:

The ideal solution would be for Mail to operate how it used to operate: Users should be able to delete messages from the Inbox, without having the “All Mail” folder visible in Apple Mail.

My Gmail still works this way. I don't have All Mail visible in IMAP and I can delete from the Inbox without issue.

Are these straight Gmail accounts or are they some type of organizational account hosted on Gmail?

I am having the same problem - basically all MOVED email stays in INBOX, not a desired IMAP behaviour.

Could someone please fix this?

I'm having the same result. It makes for an impossible "Inbox Zero" scenario.