Our new 1983 300D ("Ben" 140,000 miles old automatic) is having a rattling noise emanating from below the gear shifter.
At first I just assumed it was something in or under the ashtray as I was in the process of repairing the radio, but now that that job is complete it is apparent that the noise is coming from the transmission directly under the shifter.

The ratting noise rises and falls with acceleration.
Has anyone had this problem? What can it be?

The shifter bushings are toast. There are some in the shifter mechanism itself, or more commonly, there are 2 underneath the car that tend to go AWOL. I'd check the ones under the car first. The parts are cheap to replace, but kind of a PITA to install.

__________________
Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]

I have some replacement bushings and have just purchased the bushing pliers from PeachParts but I am not familiar with the ones under the car.
My other W123 that are in need of the bushings under the shifter are in much worse shape but make no noise.

The ones under the car come from the drop arm on the shifter, the other one being on the shift lever on the side of the transmission. When they go south, you'll get a "click" when you shift through the gears and that metallic rattling. The bushings under the car live a much harder life than the ones inside the car being exposed to the elements, road grime, heat, salt, etc.

__________________
Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]