1991 Mercedes 350 SD Transmission Problem
 

Transmission, when in passing gear, does not shift up, causing the rpms to go high with no increase in speed.

Are you holding the kickdown button? If so, you have to let off of it to shift up. Check your bowden cable, if too tight your shifts will be late and at too high of RPM. This car should NEVER shift ANY gear higher than 4100 RPM.

Additionally, unless you're doing less than 55mph, you should not be forcing a downshift for passing. It sounds counterintuitive, but all of this engine's torque is at low RPM. You'll actually accelerate and pass FASTER by staying in 4th. Seriously, time it, 55-70mph is nearly 3 seconds faster by staying in 4th gear than by dropping down to 3rd and shifting back up to 4th.

There seem to be two problems:

1) No upshift. 2) Slipping/flaring.

OP has not stated what speed they're going when this "downshift" problem occurs. If they're somewhere around 60-65MPH, this is expected behavior with this drivetrain if they're holding the kickdown button or the bowden cable is badly out of adjustment. The 3.4L falls on its face above 4100 RPM and will gain no speed with the engine roaring.

W126 automatic transmissions are notorious "slippers".