I think it depends a bit on when were you there the last time and if you experience any issues with the doors, e.g. glass lifting, door locks working, rattling. What I looked at this winter when I opened the doors:
1. Are the guide jaws fitted to the glass (this is the most important point that Garry wrote about)
2. Certainly if the locks or shifters do not work properly - that requires attention
3. Condition of the plastic parts such as slides - are there rattles and if so, is it possible to eliminate them by slides adjustment (the slides are difficult to see without removing of the glass)
4. Slack in the window shifter - there are plastic parts too
5. Condition of the rubber rod holders and their plastic sleeves
6. Some cleaning and lubrication may be needed of the shifter mechanism and/or locks/rods
7. Any glass adjustments (but then you need to remember the order: door adjusted to body, glass to hard top, soft top to glass)
8. The foams in door handles might have deteriorated - you may want to replace them
More advanced, if you want to get into it, is the play or slack on window shifter - in my case it was the key reason I could not fully close the windows with top on. I had to replace the pins. Usually replacement of the plastic washers helps.
If you are gluing on the insulation/dampening - I do not know if the stiff plate is easy to fit there without dismantling the shifter. Soft mat is easy, but the rigid plate - I do not know. It is absolutely critical to de-grease the inner door skin surface well for the glue to hold.
As for the sound dampening, IMHO, nothing is going to get rusty - when you are caught in the rain from time to time or wash your car from time to time - because of sound dampening mat in the door. I have it for some time now. Same rules, by the way, apply to overall sound dampening of the entire car.