I've been putting up with an annoying iTunes error when trying to sync my iPhone 4S. The sync always fails, telling me that it's because "Apps installed on the iPhone could not be determined" - We figured there were others out there receiving the same message, so we wanted to share how we fixed it. The problem would always start with iTunes attempting to transfer apps from the iPhone that it says weren't in the iTunes library - however, this is incorrect, as each time it wanted to transfer over all 153 apps from the iPhone. After the transfer started, the error would appear. Here are some things you can try if you're experiencing the same problem:
First, make sure you're running the latest version of iOS and iTunes. Restart your iPhone (or other iOS device) by holding down the home button and the sleep/wake button at the same time until the Apple logo appears. While it's rebooting, quit and restart iTunes. For some, this will usually fix the problem, but for us it didn't.
The next step is to reboot your computer. When it's back up, launch iTunes and update all apps in iTunes and do the same on your iPhone. Once this is done and both devices have the latest version of the apps that you own, connect your iPhone (and be sure you're using a first-party Apple sync cable) and attempt to sync. This will fix the issue if your iPhone and iTunes each have different versions of an app that might be corrupt. However, in our case, things were still failing. In this case, I had to watch the iTunes status during the sync and noticed that the error came up when it attempted to sync the Price is Right app. I manually deleted it from my phone, synced again, and it worked just fine.
Hope this saves some of you guys out there some frustration!