The MB central locking works by vacuum. There is a vacuum pump, probably under your rear seat bench inside foam protection. This sucks the doors open and closed through pipes running to each door and the trunk.
Firstly check there is no aftermarket alarm system installed. Mine is connected into the central locking, and I think it's when one of the voltages goes 'high', the car unlocks.
I guess you could try locking the car, then disconnecting the battery. Then if the doors still unlock, it probably isn't voltage/electrics related, and so it's most likely a vacuum problem in the system. I expect there should be a failsafe which should stop the car unlocling all on its own if there's a problem with the vacuum, so I suspect there may be a bad connection causing 'high' voltage to go to the relevant wire.
Perhaps someone who's worked on their c locking can remember the wire colours and purposes? I worked with mine (wiring alarm) 8 months ago
2.5-16v 1990 90,000m Astral Silver
2.0E 8v 1986 107,000m Black