Getting stuck at the "Registering Player" message when loading the Flight Crew screen is caused by an error connecting to your Game Center account. This can be as simple as a poor internet connection or an issue talking to your Game Center account. To troubleshoot, try rebooting your device and then go into your device's Game Center Settings and log out and back into your Game Center account.
If this does not resolve the issue, please check your Game Center username. If there are any non-alphaneumeric characters this can cause an issue with Pocket Planes. Some issues have been reported with emoji characters, and the @ and ' symbols. If you have one of these in your Game Center name, try taking the character out of your Game Center name from the Game Center app and the try to access the Flight Crew screen again. Once you can see the flight crew screen you can change your flight crew (to any new or existing crew name). You will then be able to re-add the problematic character back to your Game Center name if you wish.