I bought a 2001 F250 crew cab long bed, 2wd with limited slip rear end,and the 7.3L, automatic. Mileage is 48k. I've had it for about three weeks and notice this issue. When I'm stopped and accelerated while turning like going around the corner after being stopped, I get a vibration. It happens when turning left or right but not when going straight. It doesn't happen in the dirt. THe rear tires do not break traction. It only vibrates a short time until I get going above 5 mph or so. I don't notice as much when I have some weight in the bed as when I'm empty. I notice it more if I'm on an incline while making a turn. I have always had this since I bought the truck and it hasn't changed in in severity. Tires have very little mileage on them and are in very good condition. I never had a vehicle with limited slip and feel this is what I'm feeling. Any input or feelings on the subject are greatly appreciated!!!!!!!!!!!!!  

Here's what I found out. Ford says there is an additive for the rear differential that helps with the clutches grabbing, that is what my problem is. My 3/4 ton required 2 bottles @ a cost of $9.00/bottle. Seems this is a common concern with the limited slip rear ends. This is also a re-occuring issue. I drained all the fluid out of the rear diff., reinstalled the cover and added 3 qts of 75w140 synthetic gear oil @ a cost of $16.00 per qt. plus the two bottles of friction release and viola` no more grabbing!!!!!!!!
Hope this helps someone else out when the time comes.