My '88 Supra.
Sometimes, if I turn the wheels and come to a stop, when I go to start off again it feels like something is loose in the rear end. It's like a shift from one side to the other. This car has the LSD option.
Of course, I crawled around under the car and everything is tight. I need to bleed the brakes, and probably need new pads and rotors for the rear, but that will probably wait until spring. When I do lift the rear end, I'll check the shafts, but when I had it up last year they seemed fine. A cursory check shows boots OK, no rips or tears.
I have access to another LSD rear end. The current one is full of gear oil (fresh drain and fill last summer) with a proper LSD additive. When I first did the change last year, it went away for a short time.
I checked the level the other day, and it is full.
Maybe I'll try some more additive...?