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4. Pull the door trim away from the door by removing the push fit fasteners around the sides and bottom of the door (use the large flat bladed screwdriver to lift the trim and then get your fingers in and pull either side of each fastener). Be careful doing this as they are plastic fasteners on a wooden board and break quite easily.
5. Remove the door trim by raising it at the front first and then progressing to the rear. As you pull the trim away from the door remember to disconnect the speaker wiring.
A screwdriver can both scratch the door paint, and pull the fastener bases off the door card, where they are only held by epoxy which can pry off:
http://i49.photobucket.com/albums/f280/vintagefortytwo/BMW Z3 Related/Doorpanelfastener_zpsa53600a0.jpg.
I first roughly located the fasteners:
http://www.bimmerfest.com/forums/showpost.php?p=3845005&postcount=58
and then used a flat forked plastic prying tool made for removing trim.
I lifted the door card from the rear to the front, following these:
http://www.waycoolinc.com/z3/bimmerdump/62178.html
http://www.badenscarpages.ca/m-roadster-stereo-upgrade/ (Begin reading at #27)
With the card off, I found one speaker had broken from its little mount in the plastic grill mesh, so I ordered another speaker (comes with mount). I did not need to remove the grill, but I think one end snaps in and the other has a screw.
I used this occasion to remove the plastic membrane, lube the plastic window sliders, replace the rubber gasket under the outside door handle, clean out the bottom of the door and the drains at each end, re-adhere the foam cups protecting the door pulls from water, and replace the plastic sheet membrane with the later rigid foam membrane.
In reinstalling the card, I noticed that the upper end of the door pull was loose. The base of it's screw mount was broken, and the plastic post with its melted flared end was also broken. So I ordered and new door pull and installed it, and repaired the old ones' base with epoxy which won't be as strong as new. The plastic post from pull to panel will have to be replaced by a screw from panel to pull, if and when the old pull is used again.
http://i49.photobucket.com/albums/f280/vintagefortytwo/BMW Z3 Related/Z3 Door Pull Handle/32Pullbaserepair2_zpsaf8fb0b8.jpg
When replacing the card, coat the rubber gasket across the top of the door with silicone (clear dielectric grease). The card will slip in easily, and also remove easily the next time.