The blue stuff is a low friction anti-wear coating. When working correctly, parts fit together correctly, not overloaded, not contaminated, etc. it allows the slip yoke to slip smoother and less wear on the slip. Under extreme (overload) conditions the plastic has been known to squeeze out. Not a fault of the coating, a fault of whoever speced out the slip yoke for not picking one with the correct torque rating.
The plastic falling off is a failure. Chipping it off and putting it together will be a sloppy fit and is basicly putting together a worn out slip joint. It will vibrate because it will never run true.
Trying to figure out what happened. Being that it is a full splined shaft the seal should have been splined as well. You should be able to unscrew the cap on the female side to access the seal. The plastic coating looks to only be partial but the wear looks like the slip was over-compressed. Don't know if it was ordered right and later squeezed by some swap, speced wrong, or built wrong. By chance was this built as a long travel driveshaft?
At this point if you want it fixed right it needs to go to a drive shaft shop. Maybe not the one it came from. The slip needs replaced. If the CV is bad, probably best to just get a new shaft built. Lots of power and gearing in front of the shaft? Let them know and the slip may be upsized to handle it better. You really should walk in with 3 measurments. Fully compressed, ride height, full droop. That way they can get the travel correct. If all you give them is ride height they will set that to about mid stroke. Which may not be enough travel in one or both directions.
