Photos not saving to camera roll - iphone 5s

I upgraded to the Iphone 5s from 4s now photos are not saved to the camera roll. Took it to the Genius bar and they restored to factory settings, same problem but they later did a "deep restore" and it worked. When they restored my data, it broke the camera roll again. The only soultion seems to be to "start over". But this is not acceptable. How can I transfer some of the app data (texts, voicemails, and select apps) to the new phone?

Alternatively, how can I "fix" the camera roll?

Some hints: There is a folder in DCIM folder (when viewed with the app iExplorer) called 101APPLE that contains 49 phots and 2 movies from 2010 that I CANNOT delete. Iphoto wont delete them, they wont delete from the phone UI, and they cant be delete with iExplorer - in all cases it SEEMS like they delete then pop right back in!!