Welcome to the world of Swing...
Do I need to worry about this kind of thing in the GUI, or am I thinking too hard.
You probably do not want users booking the same seat twice , but how you handle it is up to you.
If you create a separate thread to do the booking, you will have a more responsive networked client, but you will have to do something to ensure that only one transaction is outstanding at any given time.
If you do not create a separate thread to do the booking then there is no way that the user will be able to book twice. But then there is the risk that the system may appear unresponsive if there are network problems.