It is just barely possible that the new iTunes fixed the problem. Here's why I say so.
Until I installed the new iTunes, I could never get my iPad (3rd gen) to sync via WiFi when it was connected to AC power--the only time it would sync was when it was not connected to AC. iOS 6.1 did not solve this problem.
This morning I installed the new iTunes and ran it. The iPad was not connected to AC. In the past, iTunes would have recognized the iPad. This time it did not do so.
So I tried putting the iPad in its charging dock. Much to my surprise, iTunes recognized it and immediately started syncing with it. This has not happened since I installed 6.0.
As many other people have noticed, it is entirely possible that this behavior is temporary and it will soon break again. Nevertheless, this is clearly a change in behavior and I am hoping it is for the better.
I guess I should install iOS 6.1.2 as well and see if anything still works.