The "curl" of the nylon material flopping from the nut doesn't hurt anything, but I agree that it indicates the nut has been off.
It is possible that the nut could be loose enough to be leaking. My little Makita battery impact seems to only tighten to around 20-22 ft/lbs. It could never remove one of those flange nuts, but not all little impacts are the same.
It could indeed be that it was simply loose. Look for nicks and burrs where that flange seal mates the output shaft and the seal lip on the flange.
Some builders routinely glob RTV under that washer saying that way there will never be a leak there! I like things clean and original, so I find it a royal pain to scrape that sealant out of the hub of the tail flange. However, one must do what ya 'gotta do' to finish the job!
On removing the rear seal, the tail housing is always off for me, so I use a big open-end wrench and just pop it out. The original rubber clad seals come out pretty easily. It is those metal-rim aftermarket seals that are a big pain to wrestle out! I've always thought I might try screwing a drywall screw into the seal and then use a claw hammer to pull it like a nail if I had to remove one with the shaft still in the middle.
Like I said the OE seal comes out without much stress. Hmm, you could probably angle a large screwdriver through the inner lip and flip it out. But when prying like that it is possible to put a big scratch in the bore that might cause seepage around the outside of the new seal. If you do see a scratch, smooth it out and rub a little sealant in the groove to be sure it seals.
Stan