Plot hole: Mario is arrested in the beginning of the game after Shadow Mario frames him for the evil paint. But before he is taken into custody, he gets his Super Water back pack called F.L.U.D.D. It is a high pressure water apparatus and a potential weapon. Yet at Mario's trial, and when he's in jail, he still has F.L.U.D.D on his back. The authorities would have taken such a device from him in this situation. Even in a fantasy world such as this, it does not make sense for them to let him keep the artificially intelligent water cannon with him during his trial, much less in jail.
Revealing mistake: This happens in the cutscene when Mario and his friends came out of the plane. When the camera is filming Mario, Toadsworth and Peach, look at Peach's ears. Her earrings are replaced by her eyes. Later, her earrings appear back.