Plot hole: When the radar man of the USS Cayuga describes a radar reading to likely be "One of the Russian cruisers", the commanding officer of the USS decides not to pursue it saying, "We are after bigger fish today - I want the Vasilyev". In the film, the Vasilyev is depicted as a destroyer, which is a smaller and lighter ship than a cruiser. In this context, the cruiser would be a "bigger fish" than the Vasilyev and the CO should pursue it instead if he was after the larger, more dangerous vessels as he seems to declare.
Plot hole: Tom discovers Claire's body in the wardrobe of his motel room. He leaves the room, and within a minute returns to the room, accompanied by the police. The body has vanished from the wardrobe, but given how little time Tom was away from the room, it is impossible for someone to have moved it, particularly given the weight of a corpse.