"Unknown error" constantly, seems tied to user preferences
This was apparently caused by an almost complete but failed deployment of the app folder. Only a few files were missing/corrupted so Craft still worked other than the issue described. 

I replaced the entire craft/app folder (deleted it, unzipped Craft on the server and used mv) and updated the permissions. At this point I got the same error. The error continued to show up after disabling all plugins other than Commerce. But when I disabled Commerce I was able to check for updates again (Craft was already up to date), and under the limited user the errors no longer appear. Oddly, re-enabling Commerce changes nothing. I did encounter a PHP error when navigating within Commerce, so I followed similar steps to upload a fresh copy. Everything appears to be working correctly now.