Can't exit airplane mode
This problem usually occurs when, for whatever reason, your phone is set to only use WiFi to make calls in the call preferences menu. On Android, with Jelly Bean upgrade, some apps will alter this setting apparently. Here's the fix. Enjoy!

From home screen, access Apps/Settings/More Settings/Wifi Calling (Press the part to the right of the on/off button to open another menu)/Connection Preferences. Choose either "WiFi Preferred" or "Cellular Network Preferred". Make sure the phone DOES NOT have "Never Use Cellular Network" selected, or every time you shut down your WiFi or go out of range of it, you'll be listed as in Airplane Mode in the on/off menu, but not in the apps/settings/.. menus, because your cellular transceiver is disabled by that setting. Note: These instructions and menu layouts are specific to my Samsung Galaxy S2 with Android 4.1.XXX Jelly Bean, but can easily be adjusted to other phones.

Hope this helps, and my best to all!