I had the same problem on my 1990 M5 -- it is LHD, but still the problem was with the passenger door.
After 2 hours of fiddling with the door card removed, some WD40 / RP7 (or whatever spray lubricant you use) and most importantly, a 2nd helper to be on the opposite side of the car, working the key in the door lock,
all that was required was a little fine adjustment to the lock frame.
Be careful with the frequency of locking / unlocking, as if your helper deadlocks the door & activates the alarm mode (2nd position in lock) too many times quickly, the central locking will freeze for several minutes.
This is time to have a break and a drink/refreshment then back into it.
It was frustrating & awkward, but for some reason adjustment was needed, just 'a bee's appendage' worth of adjustment to be technical.
Now the central locking works as it should on all doors.
Moving house is NOT the right time to try to do this. Just be a gentleman for a little longer and unlock the 'passenger' door first !!
cheers.
UltimateM