Can a Cohen who is married to a giyoret (possible an invalid one) perform Pidyon Haben?

Shalom, The mitzvah to redeem the first born child by performing a "pidyon ha-ben" with a Cohen is a very important mitzvah from the Torah. Ideally one should choose a Cohen who has a very clear tradition of coming from a Cohanic family, and who is a talmid chacham – a learned Jew. But these qualities are not absolute requirements, and one may use any Cohen, even an unlearned one. However, a Cohen born from a forbidden marriage (for example, his father married a divorcee), or a Cohen who does not keep Shabbat, are invalid for the pidyon ha-ben mitzvah. So too a Cohen who is married to a woman forbidden to him, such as a convert or divorcee (all the more so if the conversion was invalid). Once the Cohen repents and corrects his ways, he is valid again. (see Yalkut Yosef, Sovah Smachot, volume 2, 305,57 – in the name of "Pidyon HaBen Kehilchto" 5:19). Of course, you should take every care to apply this rule without causing argument or strife. Blessings.