Drivetrain Noise, Possible diff problems

[Stuffing]

As I drive along in first and second, over 10 or 15mph, I start to notice a sharp, irregular, metallic clanking from somewhere underneath the car towards the rear, possibly on the passenger side.
I took a look at my differential to see if there might be something going on there, and noticed a few things:

1. There is black sludge coating the bolts and output flange on the passenger side. It also seems to have been flung around as the wheels spun. I checked the oil inside the diff but it looks pretty clean and clear, not sludgy.
See picture here.

2. The bolts on the passenger side were ALL broken loose, but not exactly falling out. Tightening them did not eliminate the noise.

3. There is a large amount of play with the output shaft on the passenger side. The shaft is moving upwards of an inch or so. The flange on the diff has about 1mm of play. There is NO play on the driver side output flange or shaft.
See video here.

I'm thinking one of the bearings and/or seals on that side might have failed, but what are your guys' thoughts? What will I need to replace?

[Supratreo]

It's normal for the axle joint to move that much but it looks like the grease from your CV joint is leaking.
Did you check the center support bearing?

[Stuffing]

I did a while ago, it's pretty much brand new and I thought it was bolted down tight. The marks on the driveshaft are lined up too. I could check it again to be sure.

[jeffnhiscars]

If the half shaft bolts get loose there's nothing keeping cv grease from flinging out as the axle turns (AMHIK). Best practice is to use some loctite blue on those hex bolts for obvious reasons. It also doesn't look like the flange seal is leaking.

As far as flange play there shouldn't be THAT much difference between the 2 sides. It's easy enough to unbolt the half shaft (don't let it just hang) at which point the flange literally just pries out. If you go there may as well replace the seal and Oring although I bet you have a bearing problem if not a CV