Q The Activity bar in Mail often tells me that I have some incoming messages, and the blue bar tells me that they are being downloaded. Why then do they not appear in any of my mailboxes?
A This all depends on whether you only use Mail to connect to your iCloud mail account(s) using its IMAP protocol, or you also use it to collect from third party services using the POP protocol too.
If the latter, then it may be an issue with those mail servers. Mail polls the servers to see when messages are waiting; if the server gives the wrong answer, Mail displays that incorrect number.
iCloud and other IMAP servers should not make such errors: if iCloud does, contact Apple’s support.
Updated from the original, which was first published in MacUser volume 29 issue 6, 2013.