I was going to ask about whether it also disarmed the alarm, but you already volunteered that answer. Since the behavior is "unlocks all doors and disarms alarm", that narrows the problem. It has to be that one of the switches that detects the key turning, or some associated wiring, is bad and sending a false trigger event. From my 1986 300E, I think the that there are only two places from which you can trigger the "unlock all doors and disarm alarm" action, the drivers door and the trunk. I'd have to double check the manual to be sure, but I don't think you can do it from the passenger side door. That means you're in for some circuit chasing, but at least the number of branches is small. Or the car may be haunted. You never know.