"Adjudicated" means that there was a legal process and that this isn't non-judicial information. It has never been the tradition in the US that mental defectives have rights under the 2nd Amendment. (Ann Coulter thinks that mental defectives shouldn't have 1st Amendment rights either; but how could we make fun of liberals if they aren't allowed to say anything?)
Is there any basis in the Constitution for denying rights to a particular class of free citizens? It seems that with regard to this argument there should be two classes of individuals: those who pose a greater-than-average threat of committing violence, as judged by past behavior; and those who don't. The first group can be further subdivided into the sane and the criminally insane, but in either case they belong off the streets. As for everyone else, the Constitution should apply as written.
It is wrong to assume that anyone labeled with the broad brush of "mentally defective" is going to go berserk and start shooting people. Are we going to deny someone his rights on the basis of low self-esteem, bulimia, or a learning disability? On the positive side, this law would mean no armed body guard for Rosie O'Donnell!