Can birthparents contest a finalized and proper adoption?

We had some similar questions re: birth fathers. I found out, in the process of our adoptions, that the legal father need not be the BIOLOGICAL father, and that a child may have no legal father, but an identified (but not confirmed by DNA) birth father who doesn't choose to acknowledge or act on the possibility that he may be the birth father. Also that if a man who knows he is not the birth father allows his name to stand on the birth cert, then he is the father dealt with in court proceedings, particularly if the mom does not know (or doesn't name) any other man as the birth father. I got so confused after a couple of the legal tangles involved when we were adopting that I'm amazed that the courts, agencies and other concerned parties can keep any of it straight.