One possibility might be an incorrect address in the config files somewhere. Which applets specifically aren't loading? If they are OPL problems you could give paths.
If you us the Developer tools on your browser ( View->Developer->developer tools on Chrome ) you can get a record of requests made by the browser for loading additional files (including applets) and see if they succeed.
Error messages in the apache error_log might also notify you about a request that was to an incorrect url.
Out of curiosity does your LibraryBrowser work correctly? Can you add problems so that they are actually added to the sets? If not that means there is something wrong with the AJAX addresses. The most likely suspect is that $server_root_url might not be exactly correct.
One last thing -- did you also update the pg software repos when updated the webwork2 repos?
Hope these questions give you some clues as to what to look for.