Definitely check that you have vacuum at the modulator. If you have an extra rubber tee, attach a vacuum gauge and go for a ride. As mentioned above, you should have 12-15" of vacuum at idle or when coasting. WOT should be 0", and anywhere in between should have a value between 0 and 15".

Since the vehicle is new to you, it may be a good idea to start with a transmission service. Change the fluid and filter. Drain the torque converter as well. Install a new pan gasket and dump in fresh fluid. Dexron III. Use something cheap if the fluid you drain was pretty nasty, you'll want to change it again in 5000 miles or so.

Also do a search for the K1 accumulator spring. It's well known for falling apart and causing sloppy or delayed shifts from 2-3. It's possible a previous owner overcompensated for the flaring by turning the modulator up way too high.

My SDL went from "shifting by Helen Keller" and feeling like being rear-ended with every gear change to being extremely civilized "slightly firm" just with a fluid and filter change.

__________________
Current stable:
1995 E320 149K (Nancy)
1983 500SL 120K (SLoL)

Black Sheep:
1985 524TD 167K (TotalDumpster™)

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