I am new to a 1996 960 with 62K. When I'm backing up the car with the steering turned, at low speeds (out of the driveway or out of a parking place) the car "shakes" as if the wheels are not tracking properly. For those of you with 4 wheel drive, it feels like a car driven in a slow turn on dry pavement with the 4-wheel drive engaged, like sort of a gentle lurching. It does not happen in the forward direction, regardless of how much the front wheels are turned. In reverse, the magnitude of the problem is proportional to the amount that the steering wheel is turned.

A local foreign auto mechanic suggested that it was a function of the limited slip differential and wide tires (Sonar 205 55/R16). Any ideas?

This is "normal" to some degree. If the back end rubber bushings on the lower control arms get old and weak the symptom will get worse.
--
'96 965, 16' wheels, rear 18mm bar & Koni + 204HP cams at 124K. Had '85 745 Turbo Diesel for 200K.

Reverse Ackermann. When turning, the inside wheel has to track a tighter radius than the outside, so steering linkage causes the inside wheel to pivot more - going forward (named after inventor Ackermann). When backing, the same mechanical linkage causes the inside wheel to attempt to scribe a wider radius than the outside, forcing tire slippage felt as lurching/pulsing. More pronounced in 200/700/900 due to design for tight turning circle.
--
Tom - original owner '84-245na; ipd 25/25 sways; full gauge set; 292K miles and Rolling

I have a '97 960 with the limited slip rear end (standard this year) and mine does the catch/grab kind of thing when I turn tightly going forward or reverse; My driveway is gravel so I can tell when the rear end locks and unlocks really easily by the amount of gravel that crunches when it performs. I like it because I know I'll have a good chance to maintain traction on slippery roads.

Try coasting in neutral (down a hill/in parking lot) see if it changes w/o driveline input.