radio does not turn off

It might be a defective system. If you bought it from a Ford dealership I'm sure they'd replace it.

Sound like it is wired to a 'live circuit'. A 'live circuit is one that always has power when the ignition switch is OFF. But with modern radios I agree with BuiltTough. It is defective or the door open circuit has ben detached to it. Previous to (I think) 2002 radios were attached to switched circuits where the ignition had to be at ON or ACC to feed power to the radio. Modern radios are hooked to live, and are supposed to shut off when you open a door. If still under warranty take it to your Ford dealer. If not, follow the lines to the fusebox. If someone added an accessory, like XM radio, it may be holding the cirucit open. see http://www.mustangcollective.com/showthread.php?t=26033

This happened with my daughter's 08 Mustang (V6) recently. There were other things happebning as well. The panel light stayed on, and the remote wouldn't open the the trunk or activate the panic alarm. When I ran a diagnostic, no codes were reported, so I shut off the ignition, removed the key, and went to unplug the OBD2 meter. That's when the radio and dash light went off. Actually, the dash light blink on and off a couple of times. I realized that it was a wiring issue somewhere in the area of the OBD2 plug. Playing with the plug temporarily fixed the issue. I plan to remove the panels and try to secure the wires better. Also, an overflow of condensation or rain water in drain ports could be shorting out the wires, so I will check those as well.