Its hard to tell from the pictures. You need to watch the black parts to be sure its just bruised and not necrotic. If it starts to spread you will need to see a vet asap as it would need treatment and/or possible amputation.
You can put neosporin on to prevent infection, be sure is plain neosporin and not the pain relieving version.
You can try taking a wet Qtip and setting there for a few seconds and gently rubbing it. It's really hard to tell if it is in fact leftover shed. Tail shots are a little difficult to see and my vision isn't the greatest! Haha!
How this area is indented on both sides of the tail make me think this is possibly retained shed. Could be an injury and if it is i would leave it alone at this point. If this is retained shed you will want to follow what some have stated as wound treatment for moistening the dehydrated skin. You will want to remove this is it is.
A similar thing happened to my panther's tail after I first got him. I was advised by the breeder to put neosporin on it. It helped SO much and now his tail is almost back to normal. In my opinion, his tail looks better..