Don't know how common it is for the insulation to be brittle/loose. Haven't heard any mention of that. Maybe run a good rubber/leather renewal product over it?
Nowadays, doors can be part of the drainage systems, so it is POSSIBLE that it is normal for the SHO, but don't know for sure. If it's not condensation making it's way down the door frame/jamb, it's got to be a clogged drain somewhere. The closest thing to a drainage problem has usually been the sunroof after a rainstorm draining into the interior.