It seems that the latest versions of vbulletin are very broken in PHP 5.4 even though they state that "vBulletin 4.x requires PHP 5.2.0 or greater and MySQL 4.1.0 or greater"
Most of the problems are from E_STRICT which is part of E_ALL in PHP 5.4, but vBulletin and Internet Brands (who own vBulletin) seem very slow to fix these problems. They even denied that it was a problem with vBulletin when I originally reported some of the errors in June 2012 stating "Closing this issue because it appears to be unrelated to vBulletin code."
They have since reopened the issue and it has been rolled up in a PHP 5.4 check task, but seems quite slow being that PHP 5.4 was released nearly a year ago and PHP 5.5 is due out soon.
So to get vBulletin working without errors on my sites I have to modify and fix all of these problems. I wish I could contribute back to vBulletin or to its users so that this effort is not duplicated, but there doesn't seem to be a way to do it (hosting files on here would violate copyright).