Overwatering would be signified by root rot, which would appear on the top most leaves of the plant first, moving down to darken the rest of the plant from top to bottom.

Your Nepenthes is a young plant that has not yet created a woody vine. The darker coloration might just indicate that your plant is likely about to develop a brown woody lower vine as it moves its growth point up.

If the dark coloration does not look like part of the plant, it could be fungus or mildew. If so, most of the discoloring fungus that people see on Nepenthes is actually growing due to the nectar the plants produce and do not usually harm the plant itself. If in doubt, use fungicide or wipe it off with soapy water and a paper towel. If it wipes off, it is mildew or fungus, if it does not come off, it is likely a natural part of the plant. Keep an eye on the new growth. So long as the plant is growing and developing new leaves and pitchers, it is probably fine. If it slows down too much and stops developing normally, something is amiss.