a treifa food which itself is partially spoiled is cooked in a kosher pot. this food is giving a detrimental taste to the pot. As the food is being cooked by itself does the pot need to be kashered?

Thank you for your question, Food that gives a detrimental taste is not forbidden ("noten taam lefgam – mutar"). According to the Shulchan Aruch (103:2) if the food that was cooked in the pot gives off a bad (detrimental) taste, the pot doesn't need to be koshered. However according to the Rema, the pot does need to be koshered in any event. There are two reasons that the Rema is stringent about this: 1. If one doesn't kosher the pot he might eventually avoid koshering a pot that even absorbed a good taste. 2. It is possible that one might cook something in the pot that will be affected in a positive way by the detrimental taste and thus rendering it a good taste. All of this ruling is if the food is worthy of being eaten. However, if the food that was cooked was not even worthy of being eaten by people than the pot doesn’t need to be koshered at all. See all this and more in the book Maadanei Hashulchan.