I'm having a similar problem on my '88 300e. On mine though, none of the locks will unlock all of the doors so I have to open each one manually. I'm not sure if my alarm works, but I'll check it.
I have a shop manual which shows the vacuum supply under the rear seat, so this weekend I will pull out the seat and see if the vacuum is turning on. If it isn't then I will check the electrical connections. If the supply does turn on, then I will assume that it's a leaky vacuum hose somewhere.
Anyway, if somebody has any other ideas I would appreciate it.