Power divider bad…how to know?

The axle housing also has a breather. Good idea to be sure it is not stopped up. No special skills required for that. Maybe a pair of channel locks.

 

Watched your video. You definitely have a good amount of play in there. Hard to tell but looks like 1/16th or 1/8th of play or so.. And looking at the hoses or wiring in the right side of the video they looked wet with oil or grease like its been slinging oil out.

Guess you have 2 choices. Make sure its full or oil and run it. Or fix it. With that much play the seal won't last long

 

Just know that if the power divider says it's had enough and grenades itself you won't be moving anywhere without a tow

 

I can't see the video but why can't he just have someone re shim it and make sure the nut is tight?

 

Yeah absolutely worth a shot. I'm not really knowledgeable with rear ends but been told re-shimming is a temporary fix.
I'd want to see what the oil looks like.