Should a damp towel used for morning netilas yadayim not be used to 1) dry vegetables? 2) wipe face/openings?
This is fine, and there is no need to worry. Klal Yisroel has never been particular to have a special towel for washing hands in the morning, because the towel might be tameh. After you have washed your hands, they aretahor and therefore so is the towel.