I need some help trying to diagnose a shifting problem with my '85 380 SL.

The car is original (no rebuilds yet) and has done approx 170,000 mls. The car is running beautifully but ...
when I pull away it seems to pull in first then shift through 2nd and 3rd very quickly and at low revs into 4th where I then slowly gather momentum. When the car is up to cruising speed it accelerates nicely but won't kickdown.
If I use the gear selector like a manual instead of an automatic I can hold it in gear so that I can accelerate normally and initiate downshifts.
I have spent most of my life driving and fixing manuals so don't have any experience with automatic boxes thus the plea for help!

I have taken the air filter assembly off and checked the linkages to the transmission to make sure they are all in place and have not suddenly slipped out of adjustment. I have also checked as thoroughly as I can for any vacuum leaks. I have not tried getting under the car to check anything there.
I have just moved to CT and no longer have the services of a trusted Mercedes mechanic and am concerned about being 'ripped off' for unnecessary repairs through a lack of knowledge to assess what I am being told. One mechanic has suggested that my transmission is 'slipping' and needs rebuilding. I am not sure what the symptoms of a slipping automatic are or how one does slip.
Any help/suggestions would be gratefully received.