This is a problem most owners of a MGC ABS M16 or the newer M4A1/M725/M733 HW models may know. The barrel is made of several parts. The barrel itself has a metal (die cast) liner and a plastic (ABS or HW) outer shell. It parts are fixed with a roll pin under the hand guards which eventually can get loose, causing the barrel to wobble.
This is especially the problem when you have driven the pin out to clean the model.
So I recommend not to drive this pin out. You can take out the small pin, which is fixing the gas tube in the front sight, and slide the gas tube back through the receiver (bolt carrier removed). Then use the supplied tool to unscrew the barrel from the receiver. You can take out the chamber and det pin for cleaning then.
Does anyone know how to fix this problem? Maybe this is discussed on Japanese sites? I used an oversize roll pin which helped for some time, but the barrel started to wobble again.
I think you can glue it or use epoxy, but I do not like this idea much.