I'm a bit nervous to post this but it seems like I've resolved my problems with Mail in Mavericks. It was the one-two punch.
1)Reindexing Spotlight by dumping it via terminal. The "Apple Way" via System Preferences didn't work.
1. Open a terminal
2. Re-index Spotlight
sudo mdutil -E /
This did not take very long, maybe an hour and a half. I kept checking the Spotlight magnifying glass to see if it was done.
2) Reindexing & importing all my mail.
This is referred to above as RioMacUser's solution.
Quit Mail
Go to folder ~/Library/Mail/V2/MailData
In that folder remove any file that starts with "Envelope Index" It doesn't matter to where.
Restart Mail.
Mail will ask you if you want to import your mail.
Do it.
Wait. Wait. Wait.
In my case I let the process continue for nearly 18 hours. Mail, according to Activity Monitor was still doing something. But in the end I decided it was hung up, so I Force Quit it. What did I have to lose?
When I restared Mail it did not ask me to import again. AND it appeared that all my mailboxes were being populated correctly. Counts were correct. And it seemd to be happening at the speed it had in the past. Whew!
Now two days later I have not had any problems. So far...
I should say that I'd tried each of these solutions before. But not in direct succession.
Just one user's experience. YMMV.