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This is an 11 day voyage. The weight of the captain's baggage at 1m 30s seems excessive, even if he took a change of clothes for each day.
Throughout the entire movie (more specifically during the life boat scenes) Captain Phillips' facial hair changes constantly, going from beard to goatee to clean-shaven etc. However, when he is rescued he has very little stubble and clean-trimmed side burns when he was just on a lifeboat for 3 days.
Captain captors are shot in the escape boat. Blood splatters on his face, arm and shirt. When SEAL team helps him out to a boat, all the blood is gone.
At the beginning of the medic scene, the medic cuts off the yellow Navy shirt Phillips had been wearing and puts it on the counter. Later when they pan down his body, you can see the yellow shirt sitting around his waist, as if it had just been cut off his shoulders, not cut completely off.
Captain Phillips' accent seems to diminish and come and go periodically as the movie goes on. By the end of the movie he has no accent when in the beginning you could hardly understand his heavy New England speech.
Captain Phillips' beard is different between scenes after his kidnapping in the lifeboat. In some scenes he seems clean shaved (except beard goatee) and some scenes he has slightly grown beard (as would happen if he didn't shave for day or two).
Captain Phillips unberths and leaves port all by himself. In reality, there would be a local pilot on board giving steering and engine commands which the captain then repeats to his bridge crew.
Life boats are equipped with food and water for a week or more for everyone on board. Yet after only 2 days, the 4 passengers are completely out of supplies and the brown supply box appears to have never been opened in the background.
On a DDG the boat deck is on the port side 01 level. Captain Phillips is taken into the skin of the ship through the port "breezeway". There is a closer door midships, between the stacks, that goes straight to medical, the next destination for him.
The vehicle that drives Capt. Phillips to the Salalah port in Oman is shown as right side steering. Oman drives on the right and most vehicles have left-hand drive. However, the Middle East has an extremely well-developed Japanese second-hand imports market. Some of those cars go to Africa but quite a few remain in the region.
Phillips asks the pirate to be careful with his rifle (a Chinese Norinco Type 56) as the "clip" is still inserted. The Norinco 56, an AK pattern rifle, is fed from a magazine, not a clip. However, this is a very common mistake regarding firearms terminology. It would not be completely out of place for Phillips, a civilian, to refer to a magazine incorrectly.
In a nighttime shot, you can clearly see "Alexander Maersk" painted on the side of the vessel. Nine weeks were spent filming aboard the Alexander Maersk, a container ship identical to the Maersk Alabama.
After the Somalian skiff's engine breaks down, we see the American ship in the background. The ship should be moving, but it's producing no wake, so it's obviously stationary.
When a Somali pirate's shoots his pistol in the lifeboat, he does so with the hammer down. This is impossible, as it is an M1911, a single-action pistol. It can only be fired from a cocked hammer.
When the pirates attempt to board the Maersk Alabama, Phillips orders a few hard maneuvers to the left and right to throw off the pirates. We get to see a shot of the rear rudders turning. When he orders to go right, you see the ship turn right on the screen from a top-down perspective. A ship that uses his rear rudders to go right will sway left, thus coming closer to the pirate ship rather than moving away from it.
The same mistake is made when he orders to turn left.
When Captain Phillips is on deck at sea near the beginning of his voyage, the ship is obviously stationary when it should be moving.
This is an 11 day voyage. The weight of the captain's baggage at 1m 30s seems excessive, even if he took a change of clothes for each day.
The story takes place in April 2009. When the Navy SEALs are arriving at the base in black SUVs, the Virginia state vehicle inspection sticker on the windshield shows a date of 5/13. (May 2013).
At the beginning of the movie when Captain Phillips and his wife are driving to the airport, a Dodge Caravan is seen on the left side of the screen. The grille of the van is clearly a 2011 model.
At the chase scene, the Navy declares that the boat is in the direction of 035. If the boat was heading to Somalia, 035 would be just the opposite way back home as it heads north-east, and they were westbound.
At the beginning of the film, Capt. Phillips and his wife are portrayed driving from their home in Underhill, Vermont to Burlington International Airport (BTV) via a four-lane highway and passing an exit numbered 29. There are no four-lane highways in Vermont. It is unlikely they would have traveled on any highway to get to BTV. The only highway in that part of the state is Interstate 89, which does not have an exit numbered 29.
During the pirate drill, the first thing Captain Phillips instructs his crew to do is sound the main horn, to alert the pirates that the Maersk Alabama is aware of their presence. Minutes later, when the actual pirates arrive, they ignore this step altogether.
During the fight scene, inside the lifeboat, one of the pirates breaks up the fight by hitting Captain Phillips in his right side, with the butt of his gun. But when Captain Phillips is being examined by the Navy Corpsman, he complains of pain in his left side.