George,
Thank you for the suggestions. I have tried each of them with an adverse effect. Now in M the trans will shift itself 1-3 at 3k rpm. I can avoid this by shifting out before it happens. I know that this is all part of the spark chasing process. Is there any place to find a schematic for the trans control module? I would like to chase the gremlins into a "check-mate" situation, ie. close the track as I move along so they can not get passed me and make me chase my tail. I am certainly open to all suggestions, even the expensive ones.

assessing the issue. Here's the next step..
you need to pull up the wood facia at the base
of the shifter..start by carefully removing the
manual/sport mode switch and then pull up on the
wood panel..it pivots in the rear..keep that in
mind as you pull because you don't want to break
the plastic hook clips at the rear of the wood
panel. With this off, you need to do two things:
- Thoroughly clean the manual/sport mode switch
with tuner cleaner..available at Radio Shack.
- Do the same thing to the electric gear selector
switch that tells the trans computer what gear
you are in...let both switches dry before you
start the car.
- Lastly, you need to check to see if your trans
cable is adjusted correctly..pretty easy..with
ignition key in On position..motor off, stroke
the shifter through gears 1 thru Park.
The LED display on the instrument panel should
correspond to what gear you are in. Make sure
when you are in 1st..that the engagement feels
right..not too tight on the stop for example and
not to close to second..same with Park and
Reverse. My sense is your trans problem is one
if not an interaction between both issues.

Incidently, Bentley wouldn't have helped.
Be sure to report back what you find.
Good Luck,
George
90 735il/145k..since on the subject, retrofitted
my T-handle with E-36 trans shaft/pistol grip.

This has me stumped. My 88 735i with 4hp22 will drive fine in M for 1-2-3. Once over 75MPH select E and 4 takes over. No slipping in any gears. If I select E from the satrt, the shifting is 1-3 with "Transmission" displayed by the OBC. Now locked into 3, until the key is cycled. Say I start in M and get to 2 gear. If I select E here I get neutral, select M and 2 gear is back and strong. Say I am at 60MPH and I select E, again neutral until M is selected and then 3 is plenty strong. Once in 4 easy to mild acceleration is possible without downshifting. If heavy acceleration is desired the d/s is fine and u/s occurs once the throttle is eased off.
I have dropped the pan and installed a new filter and sensor behind the v/b. Fluid is at proper level. I have checked the connections at the trans, TPS, TCM, dif and crank. I purchased this vehicle second hand without an owners manual. For those of you who are Bently finatics, I have ordered mine and await its arrival. I have searched the archives and read every post that has anything remotly to do with transmissions for any 7 series. I have had the codes read and cleared by a reputable BMW repair shop.