Mail Update for Mavericks includes improvements to general stability and compatibility with Gmail, including the following:
Fixes an issue that prevents deleting, moving, and archiving messages for users with custom Gmail settings
Addresses an issue that may cause unread counts to be inaccurate
Includes additional fixes that improve the compatibility and stability of Mail
I don’t use Gmail as my primary email anymore, so I’m looking forward to reading reports about the stability of this update (will Joe Kissell tell us?). You can download it here or through the Mac App Store.