We're having a couple oddball issues and are thinking might be JSS-related. We haven't been able to confirm though.
(1) Several users have reported that their macbook pro has a frozen keyboard. I have experienced this issue myself - I would bring my laptop home, open it up, and the keyboard would not work. I could still click things away and close programs by clicking the red circle, but for something like Google Chrome I couldn't click into the program to do a full "Quit Google Chrome" because I couldn't click on the browser to get the menu options to appear. I could go into the dock and do a right-click close.
We're not sure where this could be coming from. Maybe a 10.11.4 issue? Maybe Jamf?
(2) Sys Prefs > Security & Privacy > General > we had a Config Profile set to force "Allow apps downloaded from anywhere...but due to the frozen keyboard issue deleted that entire config profile. We still don't have access to the Require password option, nor the Allow apps feature. I could understand when they were restricted by the server that they might be grayed out - but we deleted the profile that should have been doing that. Is there another location those settings might be made?