That looks like the same problem I have with my purple pitcher; traps dying, slight rot. But On my plant the bugs or mold isnt black but is brown...

Looked @ the pics, you don't have thrips. This little thing bugs, when they feed, the leave behind a mottled yellow spot that ruins the leaves, especially the young growing leaves. And when they defecate, the leave a dark kinda hard black dark brown goo on the leaf. So that is not a problem.

It looks like that it has some black mold growing on it. There is a type of mold that grows on the surface of the pithcer plant leaves where it secrets the sweet lure. It doesn't harm the plant but does tarnish it. You can't wipe it off without damaging the pitcher leaf.

But it does look like your plant was indeed the victim of neglect. Dried tips due to lack of watering and under the shade, watering with tap water to boot.

Still, your plant seems to be doing fine and I bet is is barely becoming dorman. Keep growing it they way you are doing it. Once its dormant, you can place it in the shade and water it enought just to keep it moist.

Good luck