The iPhone settings badge is triggered by one of three possible causes. 1) The iPhone operating system requires an upgrade. 2) The cellular provider has a pending upgrade. 3) Or there is a corrupt parameter in the operating system or one of the other features on the phone.
The first two were easily remedied by traditional methods, however, the third is just disturbing.
The corrective action for the third problem is a) backup your photos to iPhoto. b) backup everything else to iCloud. c) restore factory settings. d) restore from iCloud.
The reason this sucks as a solution is because apple could have published this solution instead of forcing me to visit a Genius Bar. What an amazing waste of time and justification for my desire to convert to android.