Dave, often times, movies and other media news stories frighten people away from adoption with these nagging worries.
However, in truth, adoption law is quite clear that once the adoption is finalized, the child now belongs to the adoptive parents.
Although there have been some adoption cases (that have been highly publicized), in which the adoption was overturned after being completed, it was only because the cases were full of errors, and legal action was not properly addressed, making the adoptions invalid.
(This is why I highly, highly, recommend a reputable adoption lawyer.)
These cases are rare and are exceptions. In the majority of adoptions finalized today, the birth parents have no rights to the child once the adoption is finalized.
In some states, consent is irrevocable upon signing, other states give the birth parents a set number of days in which they may revoke their consent.