This bug has been around for a little while now, and one of my clients has it bad as they cannot save user profiles without patches to WP core. (Unfortunately although WordPress Trac has tickets (#9640, #7540) the discussion over how the problem needs to be fixed has been going on for a couple of WP releases now.)
The symptoms are the following error:
Catchable fatal error: Object of class __PHP_Incomplete_Class could not be converted to string in /home/halfbets/public_html/wp-includes/wp-db.php on line 445
The solution is outlined in this WP support post, but does involve editing core WP files so does require both some knowledge and a brave heart (and the willingness to repeat the exercise if the problem isn’t fixed the next time you upgrade).