The dreaded 500 error is the bane of my existence. If your error reporting isn't kicking out anything, the first thing I usually check is the htaccess file to see if it's the problem. In your case, you can still get to things, so I suspect that's not the issue.
The next thing I do is start uninstalling and reinstalling, or upgrading stuff. I've had the Akeeba stuff break a site before and an uninstall-reinstall did the trick. Every so often that also happens with some other extensions.
In a few cases, it's been some tiny plugin somewhere that has somehow gone crazy. At one point I literally did a process of elimination and turned off loads of extensions until either I started to get error messages on the front end or the problem went away.
Also, try setting the error reporting on Development, I think that turns on messages in the back end.
Anyway, I doubt it's a permission issue as much as it is that you've got something that's partially broken in there.
Are you running JCE? if so, try reinstalling or disabling it to see if that's the issue). I recently had this issue with a site when we upgraded JCE before upgrading the joomla core. JCE didn't like that at all. I ended up pulling a backup of the site, dropping it into MAMP and then upgrading the core first, then upgrading other parts after. I broke the site several times till I finally got it right.
Hopefully these tips will be helpful in figuring it out.