Can you post pics of the kit in question - especially the areas you are concerned with? That would help tremendously. Reading the nest box eye thread has me concerned that the kit in question might have some health or genetic issues going on and it might be the humane thing to terminally cull it. Hard to say without knowing exactly what is going on though.
Is the black stuff wet or dry? I have had one or two where the cord didn't get fully cleaned up/off by the doe and they of course look totally different, then the others will have a black dot there for a little while, just like a human baby when they are newborns. It takes time for things to heal, dry up, and fall off. If it's something other than a small, dried up piece of the cord then there might be something else going on.