Is it common to have pain when rinsing with salt water after wisdom teeth extraction?

NO: Rinsing helps keep the extraction sites clean of debris if done gently. Too vigorous rinsing can result in loss of the blood clot in the socket. This is called a dry socket which is painful.

That depends: Severe pain...No, some discomfort for the first 1-2 days ...Yes. If you are having severe pain or it lasts beyond a few days you need to return to the ral surgeon who extracted your teeth. You may have a dry socket.