I know that this is supposed to be 'military' stories and anecdotes, but all my aviation experiences are from the civil world. A few 'towing' and 'pushback' events that I either witnessed, or was involved in (in a minor fashion) ...
Towing team detailed to move an airliner from a stand/gate at the terminal to remote parking as it won't be required for the rest of the day. Towing team tow the wrong aircraft ... two identical aircraft on adjacent stands, and they picked the wrong one! Red faces.
Notified of an aircraft arriving shortly and has indications of a hydraulic failure. The plan is, they will stop on the runway and a towing-team will connect the bar and tow the aircraft to the stand. The towing team are waiting near where I am working, so I spend some time chatting with them while they explain how it will all happen. Aircraft lands, and one of them says (checking his bit of paper) "that's the one we're here for". At which point I advise them that they've bought the wrong tow-bar for the aircraft. Red faces.
Sitting in our crew-room when there is a very loud and sudden 'b-o-o-o-m!' and the whole place suddenly goes quiet. Everybody does their best meerkat impression and heads for the nearest door to see what's happened. No smoke or visible signs of damage, but there is an aircraft half-way through its push-back which is now stopped mid-taxiway.
During pushback, just as they're about to start the turn, a tyre burst on the tug. A big 70-tonne brute, with tyres nearly 6-feet across. Not sure what tyre-pressure it was, but it was loud. I suspect that the ground engineer needed a change of under-crackers.