Actually the MID on the E39 might be a bit easier to take apart than what is shown in the pics for the E38. Although, because you can not hold the board alone in your hands, the space is limited for ribbon removal and installation. Still, there is enough access.
Make sure you have a set of small torx head screwdriver before you start. I bought a set at Radio Shack for 17 bucks.
It is evident what you need to do once you get inside. These are the steps I took and the ones I got stuck on, I describe in more detail. I was making it in some cases more difficult than what it was.
To remove the mid:
Pull the knob out. Inside you will see a little hole on the bottom. That is where you put in a torx wrench and turn it 90 degrees. Almost as a door knob, as you turn, pull on the volume shaft and the MID comes right out. Unplug it from the car. There is a lever in the plug that as you rotate it, it self extracts the plug.
Working on the unit:
I removed the top cover of the unit and begun taking screws out of the face plate and then the display and the nut from the volume control. There are thin spring clips used in the display as washers that you need to watch for.
While separating the face plate, this is where the white retainer plastic clip fell out from my unit and I have not been able to figure out where it goes so look for it and let me know where it goes if you can.
You need to unplug the connectors. There are two black connectors in the front of the unit that I could not take out until I noticed that they slide out sideways (towards the display) when looking at the face of the unit. The other red plugs are easy to take out.
Now you have left the scary and hard part. That is removing the retention bar, peeling off the pink foam strip, tape from the bottom and finally the ribbon cable. You might want to mark the location of the ribbon cable on the board with a marker before removing it and it will help you get started when ready to assemble.
Clean (remove the film of glue) all the connectors on the board until they shine and the ribbon cable until you see a clear film. Qtips and acetone work great! A magnifying glass is very reassuring for “challenged people” like me. Look at the pics at this point to convince yourself you are doing it right. It is hard to believe that this solves the problem.
Position and tack the ribbon cable in at least two places. Check to make sure it is all lined up correctly and tape it securely from one end to the other. Put the foam strp and retainer clip as shown on the pics and connect the plugs; use one screw to hold the display and plate and test the unit before reassembling. You can do it safely. I actually had to go back and push in on the pink strip a bit more into the retainer bar to get a 100% of the pixels to come on.
By the way, VDOrepair only deals with the odometer and will not do MIDS. Frankly, after looking at the procedure, I would give them the odometer if that was the case. On the other hand who knows? May be I would try that as well. 
Good luck and I hope the ~3 hour operation is successful.
This is my own DIY repair, YOU take full responsibility for your repairs. If you break it or the thing smokes, it is not my fault.

'03-530i - 5spd - Sport/Premium/Winter packages

• pixels!! - psiwak1 2008-08-21 22:35:30 (298 views)
  • Re: pixels!! - psiwak1 2008-08-22 18:10:13 (212 views)
    • Re: pixels!! - rick540 2008-08-23 04:33:49 (225 views)
      • Yes. - bolkow105 2008-08-24 17:50:28 (194 views)
        • MID pixels fixed! - psiwak1 2008-08-25 09:45:08 (404 views)
          • That's what I've been waiting to hear! - ZeroDfx 2008-08-26 10:35:37 (162 views)
            • Re: That's what I've been waiting to hear! - psiwak1 2008-08-27 00:54:58 (149 views)
              • A couple clarifications please - ZeroDfx 2008-08-27 09:24:02 (116 views)
                • Re: A couple clarifications please - psiwak1 2008-08-28 00:01:15 (105 views)
                  • Thank you for that; I'm good to go (nt) - ZeroDfx 2008-08-28 13:09:51 (101 views)
                    • pixels - pablo 2008-10-28 17:48:46 (19 views)
            • Take a look at..... - bolkow105 2008-08-26 15:28:31 (137 views)
              • Re: Take a look at..... - psiwak1 2008-08-27 01:01:05 (110 views)