My rear dif makes a thumping noise and I thought I'd take a look because it's very noisy while driving and then discovered this if anybody has an ideas on what it is here's the link to the video
When does the thumping occur? Deceleration/Acceleration/Coasting/Cornering? Thumping on clutch type diffs is normal (for the most part) however you're most definitely running the stock open diff (I would assume it's open since your pic shows an RS). If it's an open diff I believe this is normal. Just a little (even the slightest) more resistance on the left wheel would cause your right wheel to only spin. If you were to carefully gently touch the tire while it's rotating it should cause the other wheel to spin. Assuming it's not severely seized. Or better yet, put the car in gear (with it off) and turn the left wheel to see what happens to the right. Since it's an open or non mechanical LSD (viscous) it SHOULD spin the other wheel (the opposite direction). TLDR; I think the one wheel spinning is fine. More info on the thumping/clunking would be good, I can't really hear it in the video.
@blackozone I was going to say the same thing but I figured I would stray away from it haha. I just did this same thing with my big ass jack stands that might as well be considered a lift and I was afraid for my life. Anyway it's super hard to tell from the video, I honestly can't tell if anything is even wrong. I hear a squeaking ?! If it's under coast then that sounds like it could be a bushing if it's a thumping noise. Here's a good quick checklist of symptoms. The good news is I literally just came in from swapping my rear diff and it took me 58 minutes. So it aint no thang. http://www.onallcylinders.com/2012/03/30/quick-guide-to-diagnosing-differential-driveline-noises/
I can hear a pretty fast thumping sound. Not sure what it is, but it does remind me of a tire rubbing/exhaust rattling against the frame/etc.
Looks kinda like your left rear axle isn't popped all the way in. I've seen it before, and a lot of crazy stuff happens on automatics when that happens. I'd try popping that axle in further, if it doesn't "clunk" into place slowly rotate the left rear wheel until the splines line up. Make sure its going in straight as well.