Thanks so much for your help. I think I got it fixed. I went looking for the Unity log file and noticed that the ~/Library/Logs/Unity/ folder didn't exist. I decided to try and manually create it and got a permission denied error. Apparently, my ~/Library/Logs/ folder was owned by root and not by my user account.
Executing sudo chown john Logs from within the ~/Library/ folder seems to have fixed it right up.
Thanks again for your help!