Apple has resolved this problem by displaying the apps past the first 176 onto home screens that are grayed out. These home screens, numbere
d 12 or higher, will not currently display on your iPhone, but at least now you have a chance of grabbing apps from these screens and moving them to another visible screen. You should keep in mind that any apps on the home screens past the first 11 will only be accessible via a Spotlight search.
Problems sorting apps were not completely resolved by this iTunes update if all the home screens and the extra ones are completely populated. In this case, you lose any chance of moving the apps around effectively. However, there is a work-around–simply sync one more app back to your iPhone and iTunes will add another grayed-out home screen. The exception being that this screen will now be mostly empty giving you the work space you need to get your apps sorted the way you want them. When you are done, make sure that extra app is the only one left on th
e extra home screen and delete it once you are satisfied with the way your apps or home screens are arranged.