Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP)
Other / Unknown
Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Ground Equipment Issue
General None Reported / Taken
Human Factors
After completion of pushback and after receiving salute I flashed the landing light.  The push lead and a wing walker were observed walking away as the tug backed away from the aircraft.  Approximately 10-15 meters off the nose a small bag which apparently contained the push headset fell out of the tug cab where the bag and the headset fell apart laying on the ramp.  The tug driver saw it fall out his side of the cab and stopped.  As the tug driver stepped out of tug it began to roll towards our aircraft with the tow bar still mounted on the front like a battering ram.  The tug driver immediately jumped back in the cab and stopped the tug and manipulated some controls.  The cab driver was the only one in tug and rest of pushback crew was oblivious as they walked back to gate area.  I don't know if the tug has a parking brake but the tug driver again stepped out of the tug while it idled away from the aircraft towards the terminal.  The unmanned tug continued towards the terminal at a walking pace while the tug driver scooped the headset into the bag and then he jogged back and jumped in the moving tug.  The tug now under manned control continued back to the gate are and we taxied out for departure.I don't know if it was complacency or rushing to get out of our way or both but I would like to think push tugs both have a park position as well as a park brake both if which should have been used in this case in my opinion. Emphasize safety to ramp members to protect persons and property.
Air carrier First Officer reported observing potentially unsafe ramp procedures after pushback at DFW.