When Chandler enters the room where Quincy is being held one of the MP's goes to close the door behind Chandler. However in the next shot the door is wide open and the MP is still standing at attention, then in the next shot after that the MP is shown closing the door the rest of the way and returning back to the spot he was originally standing at.
Active radar does not rely on the target emitting radar signals themselves, but simply on reflection, so the admiral would continue to see two blips on his screen. Furthermore, although the Arleigh Burke class has a reduced radar cross section compared to similar sized vessels, this is not even close to the equivalent of a short length of tin foil, which would also produce a noticeably different reflection.
During the dead reckoning voyage through the canal at EMCON alpha, the James is shown from above with its radar scanners spinning (active). Part of EMCON alpha is shutting down active radar scanners, and Cpt. Chandler said as much when giving the order to turn off all transmissions.
When the ship entering Guantanamo Bay is identified as a Russian Kirov-class battlecruiser, a sailor incorrectly states that they were all retired. There are four ships in the Kirov-class. As of summer 2014, one is currently in active service with the Russian Navy, another is undergoing a major refit, and two are decommissioned and held in reserve. The Russian Navy currently has plans to reactivate the other two Kirovs in the next five to ten years.
The Russian cruiser is identified as the ship that launched the nuclear ICBM at France in the pilot episode. While the Kirov-class nuclear-powered battlecruiser (officially called a Large Missile Cruiser by the Russians) is the largest and most powerful surface combatant warship currently in service with any navy, it does not have the capability to carry or launch ballistic missiles. It does carry a large arsenal of cruise missiles which can be fitted with nuclear warheads.
The torpedo is shown detonating and sending a huge water spray into the air as it destroys the reef. However, just a few seconds later, the bow of the ship is shown passing through the opening in perfectly clear water. The water should be very murky due to the sand, silt and reef material that the explosion would have displaced.
The Russian Naval officers are wearing mock up uniforms - created by modifying US Marine dress tunics with Russian shoulder boards and patches. The ribbon bars are American ribbons. The 'Pershing style" mandarin collar tunic was only used by the Soviets until a few years after World War 2. Post 1950s Soviet to current day Russian Naval Senior officers actually wear black double breasted jackets, white shirts and black ties. The officers wear the "Red Guard" chest badge, which indicates one of the Guards divisions - which were Infantry and Armored Divisions designated to protect 'Mother Russia'. A naval officer wouldn't wear that.
The American ship is escaping through a canal over a coral reef, however there is no such canal in Guantanamo Bay. Also, their locations as shown on the radar screens means that there is no other way out than going right past the Russian ship.
During the escape attempt over the coral reef, one of the US Naval Officers says "We're going to hit the coral in 15 seconds." 25 seconds later she says "Ten seconds, Sir." They don't launch the torpedoes until 58 seconds after the "15 seconds" call, and they don't pass over the coral reef until the 1:12 mark, almost a full minute after they should have hit the reef.
After the tin foil trick the Nathan James is supposedly invisible to the Russian ship. The Nathan James could have simply attacked at this point instead of the elaborate decoy ship/reef torpedo escape plan.