Just posting to bump this and comment that I had the same issue - apps downloaded and set to sync, then you get the "Not authorized on this computer" message.
I followed MinFlux's suggestion of double-clicking on one of the apps.
This brought up a dialogue box to enter the iTunes password. Once I did and clicked "OK," I re-sync'd my iPhone and the applications went right across.
Since this wasn't shown throughout the natural course of upgrading to v2.0 and downloading apps, perhaps this tip could be temporarily made sticky until the message gets out?
Or am I just slower than the average bear?