I have a 1994 325i Convertible. Your problem sounds like maybe it's two different things. Here's why I say this: My passenger side door glass DOES NOT reposition upwards the last .025 inch or so when the door latches. The door glass DOES NOT drop when the door is unlatched. The interior lights don't come on when the passenger door opens, either.
The driver's door glass DOES reposition on latch/unlatch and the interior lights come on BUT... the door unlatches very stiffly (the latch inside or outside seems to take more effort than it should as compared to the passenger side - or to other like vehicles). It sounds like you may have both those issues rolled into one door.
I'm online right now doing research before I crack the door panels loose. I suspect there is a switch, probably attached to or linked to the door latch mechanism. If I'm right and that switch is faulty on the passenger door, that would explain the glass seal/interior light issue.
I'm betting that on the driver's door being stiff to unlatch, there is a door linkage issue, perhaps a bent actuator rod or possibly a piece needing some lube. I would not recommend petroleum based lubes. I will use a silicone based grease if needed. This avoids chemical damage to the plastic parts.
Any help someone can throw my way would be great!