This is an absolute disgrace. Four months after public release of Mavericks, and the Mail app is still not working. How hard can it be, when it was perfect under all the previous OSX releases? Forget all the rest: if I can't have reliable access to my mail, I can't use OSX.
I've had all the problems documented in this thread and more. Just now, my mail app just emptied itself: no messages left whatsoever, and I've had to remove and reinstall my account for the fifth time. If I were travelling and had a poor internet connection, I'd be ****ed.
I didn't even have a choice about installing Mavericks: it was installed for me by the Genius Bar after my SSD crashed and died.
Now I've got problems with my mic as well, ever since I "upgraded" to Mavericks. Apple can't fix it: it drops in and out, and sometimes sounds like I'm in a snowstorm. All we've concluded so far is that it's definitely not a hardware problem.
The days of "Mac just works" are well and truly over. If Apple can't fix this soon, I'm going to 'upgrade' to a PC. I've been with Apple now for 18 years, and can't believe I just said that.