This is an annoying task, but I finally figured out a good process. You'll need:
- A heat gun
- WD40
- A dish cloth
- A good razor blade holder
- a couple of plastic blades (ebay link)
Note that the blade holders you get with those plastic blades are junk. I used a Trojan blade holder that I already had, and it worked fine and the blade didn't shift around.
The process is then simply apply heat, use plastic blade to peel back vinyl, repeat.
Once you get all the vinyl off, you'll be left with a layer of really stubborn glue. Soak it in WD40 for 5 minutes, then heat gun and scraper, over and over, until it's all gone. If you are planning to repaint the door, you can do this last part a bit faster by using a Scotchbrite pad, which will remove the adhesive faster, but it will scuff the paint a bit in the process. I wouldn't recommend using this method otherwise, as it will leave the paint too thin around the high spots of the bodywork.
