Add me to the list of those having issues with Mavericks Mail and Exchange. A few things I've noticed:
New Exchange mail is not showing up regularly in my Inbox at home. It can take several hours before it appears. My last message in my inbox was almost a day ago now. However, Exchange folders other than my Inbox seem to update in "real time". I have my work Mac (10.8) running Outlook 24/7 and processing spam - and those messages in my Junk and Deleted folder appear at home immediately. Likewise, if I log into OWA web mail and move an item from my Inbox to another folder, it shows up right away in Mail (in the appropriate folder). So the Inbox is broken, but other folders seem to work as expected.
On a manual check, the message in the Activity window stalls on 'Fetching new mail/Synchronizing "Inbox - " '. The progress bar is stuck at the beginning. After a few minutes, this message disappears and rapidly shows the synchronizing with my other folders, which as I say, seems to behave normally.
I've also noticed the Activity stall on 'Fetching new mail/[Inbox] Requesting latest information' on an automatic fetch.
I seem to be able to send fine though the Exchange server (including attachments), though the Sent folder is not updating consistently.
Changing "Check for new messages" from Automatic to a fixed time has no effect. Turning on "Use Autodiscover service" doesn't help. Relaunching Mail does nothing. I haven't deleted and readded my Exchange account as this can take hours to resync my 20k emails (asuming it will!)...