I recently bought a 1983 300D and when I got it it was pretty low on transmission fluid and shifted hard in all gears. I put some Trans-X in it and filled the fluid level up and drove it about 1,000 miles.

Now it shifts hard going from 1st to 2nd. I heard somewhere that these cars are supposed to start off in 2nd gear unless you are really accelerating, but mine always starts in first. I also heard that there is a screw somewhere that allows you to adjust whether it starts in 1st or 2nd gear.

Anyhow, is any of this true? I could live with the problem if it started in 2nd gear 90% of the time, but it's very irritating (and probably not mechanically healthy) to be shifting so hard every time I start moving.

I was thinking it might be vacuum related but from reading some older posts on here it seems as though it would consistently be shifting hard in all the gears if that were the case. This car has 240,000 miles on it.

I believe that it is typical on that transmission for the 1-2 shift to be harder than subsequent shifts. I think MB modified the transmission to avoid that problem in 85. MB also modified the transmissions to start in 1st gear at some point. It wouldn't surprise me if yours is intended to start in 1st gear.
Harsh shifts can be modifed by changing the amount of vacuum.
This thread has a lot of good info:

It's CRITICAL... how you set your transmission's vacuum system on your diesel MBZ...

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13