I have the same problem as many other users. The displayed number of Incoming Messages shows anywhere between 1 and 100 or so but the actual received/downloaded messages can be between 0 and 10 or 20. Obviously I am not receiving a lot of messages on my iMac because I can get them on my iPad 2 or using my ISP webmail, messages show up there which never appear in my Mail.app on the iMac. But answering mail on my iPad is often inconvenient if I have to refer to previous data held on the iMac.
The 'missing' messages are nowhere on Mail.app on the iMac. Not in Archive, not in Junk.
I do not have IMAP or GMAIL accounts; just two standard POP acoounts with the one ISP. The ISP server has no problems because of the webmail and iPad mail as mentioned above.
I have tried the latest 'cure' of taking accounts off line then back on but to no avail. Quit Mail and relaunch has no fix. 10.9.1 no fix.
What to do? Wait for 10.9.2? I am so far reluctant to use third party mail apps as I always want to use Apple's inbuilt apps where possible. But this hassle is really tiring.
Yes, I have sent feedback. And rebuilt Mailboxes.