Something is messing with my disk permissions, which breaks a lot of file-related stuff. Can I find out what is causing this?
I don't know if the permission issues are related, but revealing files in Finder not working and Archive Utility stopping to respond are both symptoms of the Apple Events bug that was introduced in 10.8.2.

I don't know if it was fixed in 10.8.3, but when that starts happening, you can terminate appleeventsd from Activity Monitor or with sudo killall -9 appleventsd (without -9 other processes stop responding for some reason). The issue will probably return within a few hours or days though.