I just fixed my daughter's 87 300E odometer. Speedo was working fine but trip meter and odometer was not moving. Was easier than I thought and design was different from the DIY article that is listed in the DIY section.

#1. Basically, I just used my fingers to put pressure on the inside of each
side of the cluster box and pulled/wiggled it out until I could see
the pressure clips on the top and then pulled it out (you can
make some hook tools from a wired coat hangar if you can find one
around your house anymore).
#2. Reach back there and unscrew that brass odometer ring.
#3. Disconnect vacuum hose for economy gauge if it has one.
#4. On this one, all of the light bulb indicators had matching numbers for
each hole they went into (so did the holes) so I just pulled them out
without marking them (if not, use masking tape and mark each one).
#5. Pull out rest of connectors. They all only fit into a specific spot so
don't panic on trying to remember. Easy to reassemble and plug
in.
#6. Take the console, out, flip it over and uscrew the mounts that hold
main console to the plastic frame (4 if I remember correctly).
#7. Unscrew 2 screws from outside temp gauge and remove digital lcd
module (black skinny rectangular box underneath speedo).
#8. Uscrew 4 screws that hold speedo and odometer to board and
remove (be careful not to bend or break needle (you can also
remove needle by taking off black cap, and pulling out needle off
stem...it's on tight but will come off with steady pulling).
#9. Now...check the little worm gear (about 1" long) and white plastic
round gear for damage. If damaged, replace. Mine had worked itself
out towards end away from the worm gear. I pushed it back in.
#10. Also check the reset lever and springs for the trip meter to make
sure they are working ok. Once I did that, to test and see if it
worked, I got my drill and found a bit that fit in the back of the
speedometer disk just like the speedo cable. I slowly turned it both
ways until I saw the worm gear turning and engaging the little white
round gear.
#11. My trip meter started moving, then the odometer...just like it should
work when driving. For me, problem was solved at that point and I
just put it back together in reverse...easy.
#12. Went back to car, connected all bulbs back in, connectors, vacuum
line, big round electronic connector (only fits one way!) and pushed
back into dash. Turned on car took off and HAD NO SPEEDOMETER
FUNCTIONING! Crap, forgot to reconnect the brass speedo ring with
cable to speedometer! Simply pulled it out, reached in and screwed
it back on, pushed it back in and VOILA! A working Trip meter and
odometer!

Hope that helps somebody else!

Steve