I'm glad to say I found a buyer for my 84 240dl.

I'm sad to say that as soon as we got back from the test drive, I smelled what reminded me of hot wiring, and both back wheels were quite hot to the touch. He's still willing to buy it if I fix it, and to wait until after my final exams for me to fix it.

My first thought was "stuck caliper", but both rear wheels were hot. One might have been hotter than the other.
I did the brakes on it (just new pads on the rear) last year and drove it for a while after that. Bleeding it was horrific. The front seemed to have a caliper that might be sticking, but the braking performance was fine.

Anyway, before I go looking at the brakes, what could be wrong? The things I'm thinking of are - sticking hydraulic brake calipers, sticking emergency brake (maybe he was driving with it on?), no oil in the differential, sticking rear wheel bearings, some sort of limited slip differential I don't know about dying on me, and that's it.

There is play in the differential, but I don't think it's up and failed on me suddenly. I guess the first thing I'll do is put the back end on jackstands and see if the wheels spin or if the brakes are sticking, then check the differential fluid. Past that, I don't know what to look for. Any suggestions?

Could a stuck brake on one side heat up both sides? We drove about 6-10 miles total.

Cheers!