I was not able to duplicate this problem when upgrading to WordPress 3.6.1. However, I was able to to duplicate this exact problem when upgrading to Magic Fields 2.2. Did you simultaneously upgrade to Magic Fields 2.2?
Since, Alt Related Type, Alt Textbox and Alt Dropdown must be enabled after Magic Fields 2 is installed or re-installed a way to fix this problem is to disable Alt Related Type, Alt Textbox and Alt Dropdown (followed by a Save Changes) then re-enable them (again followed by a Save Changes).
Incidentally, Alt Audio is implemented differently and the above is not necessary. Also, Alt Audio causes problems (see AJAX scripts fail from whitespace after ?> in magic-fields-2-alt-get-audio.php) and I would disable it unless you make the change suggested in that article.
If you did not simultaneously upgrade to Magic Fields 2.2 then this explanation is not valid and would appreciate you letting me know.