Can you describe the mail problem more fully? Does Mail fail to launch, won't send, won't receive, all your mail is gone, or something else?
Let us know.
Try running the combo updater. It fixed a lot of problems for people when 10.8.4 was released.
Do a backup.
Take notes of all account information or take screen shots. You may need to set the accounts up again. Quit Mail.
Copy the line below.
Select Go/Go To Folder from the Finder menu bar. Paste the line into the window. You won’t see it.
Move the folder com.apple.mail to your desktop. You must move the entire folder, not just the contents.
Relaunch Mail and test. If the problem is solved, recreate any required Mail settings and import any emails you want to save from the folder on the desktop. If the problem remains, return the folder to where you got it replacing the one that is there.
Information learned from Linc Davis.
If you prefer to make your user library permanently visible, use the Terminal command found below.
You might want to bookmark the command. I had to use it again after I installed 10.8.5. I have also been informed that if you drag the user library to Finder it will remain visible.