When Beckett wants to interview the astronauts at the 12th precinct, in essence, she is threatening to shut down the sim by ordering people to go with her. Legally, she cannot order anyone to go with her or to even talk to her as they are not under arrest. Furthermore, she says she will get a court order, but no judge can compel them to cooperate. Since Viggo Jansen offered to cooperate fully in the investigation, she could have conducted her investigation there, which is legal. Everything Beckett threatened to do in that scene was unconstitutional and/or illegal (except when she stated she would remove the guilty party).
Murder victim Tom Richwood is described by the mission controller as a former Navy Top Gun, yet his rank in the video log is shown as Sgt Mgr.