Perm Res case to Naturalized US Citizen?

Joan marries Mike in 1999. Mike is a US Citizen/NJ and Joan is an alien from Europe. In 2001 Joan gets her Unconditional Green Card, but the marriage is not going too well, so they split up (Mike is a cheating and lying louse) but remain married. Late 2001, Joan meets Edward who is also an (H1B) alien and things go pretty well. They move in together in January 2002 and have a child in November 2002. Then another in 2006. Edward is aware of Joan's marriage to Mike, who eventually agrees to sign the divorce papers in 2006 before the second child is born. In 2007 Ed and Joan can now get married and do. Ed applies for his Perm Res through marriage to Joan and has an appointment with USCIS. However, the officer at the meeting would not approve the petition until he orders and reviews Joan's file (she is now a US Citizen since 2006). What are they checking for (it was a bona fide marriage to Mike) and what risks exist for Joan and Ed?