Helmet worn by Dengler as he flies his Skyraider is not the proper type. What's worn in the film was used by helicopter crews. Fixed wing tactical crews wore slightly narrower helmets (no bulges at the ears) which were typically white and had a tinted visor.
When flying the Skyraider, Dieter Dengler (Christian Bale) is wearing a SPH-4 Helicopter pilot helmet that is missing it's visor assembly. In addition to missing a major portion of the helmet, this helmet was not in use during the time period of the film (it wasn't seen until the 1970s), and was not used by the pilots of fixed wing aircraft.
In the supply room scene, the sailors are shown with name tapes, and "U.S. NAVY" tapes on their dungaree uniform shirts. The US Navy did not use these until 1992. During the Viet Nam Era, Sailors either stenciled or hand printed their last name above their left breast pocket.
In the supply scene, before setting out for the mission, the U.S. passport Dieter shows is not only the wrong color (blue rather than green), but is also the smaller size in use today rather than the larger size in use at the time.
Shortly after being shot down, Dengler is seen randomly flashing his signal mirror in order to attract attention. The proper way to use such a mirror is to sight the rescue aircraft through the transparent circle in the center of the mirror, which then automatically aims the reflected light right at the aircraft.
The type of aircraft changed in the crash scene: Dieter Dengler's aircraft was an AD-1 Skyraider. The tail section of the crashed aircraft in the rice paddy is most likely that of a North American AT-6 which has rounded vertical and horizontal tail profiles. The Skyraider has squared off tail profiles.
At the end of the scene in which Dieter is given the choice of signing the document condemning America, his glass of water magically gets refilled as he is taken away, and then goes back to its original level.
When Dieter enters the camp there is a discussion where he mentions that he was just engaged the day before being shot down. Later in the film there are several instances where a gold wedding band is on his left hand.
At 1:19:35 , when Dieter steals the rifles from the hut and approaches the other prisoners before their attack on the kitchen, a crew member (wearing a cap) can be seen moving from the right of the screen to the left with a camera or some other equipment.
Twice in the film Dengler is referred to as Flight Lieutenant Dengler. There is no such rank in the U.S. Navy, nor in the U.S. military. That's an RAF rank. Dengler was a Lieutenant Junior Grade, commonly called at LT JG (Lieutenant Jay Gee).
When the Skyraider crashes, the view from the tail forward shows the tail surfaces of something more like a Republic P-47 than a Douglas Skyraider. A Skyraider empennage is squared off, not rounded like a Republic or Curtiss craft.
When Dengler is rescued, he only lowers one prong on the jungle penetrator rescue seat instead of the two prongs as taught in survival training. This is explained in Dengler's book because he was "woozy and distant".
During his captivity, Dieter is shown wearing his gold wedding band - it is generally regard as something no American pilot would do. However, on the DVD Walter Herzog explains a deleted scene where Dieter's ring is almost stolen. When the guards are transporting Dengler to prison they stop at a village. A man there threatens to kill Dieter unless he gives him his ring-a gift from his fiancée. When they leave the village Dieter tells the guards his ring was stolen and they return to the village. The guards cut off the villager's ring finger and return Dieter's ring to him. This is a factual event that haunted Dengler the rest of his life.
During Dieter's shoot-down scene, when the camera cuts to the flight instruments inside his plane, the altimeter is shown winding down rapidly from 57,000 feet yet he's just above the ground. Also note, the 10,000-foot indicator fails to move at all AND the rate of climb indicator shows a slight climb.
When Dieter is finally rescued and in the helicopter, a camera angle from outside of the helicopter shows him holding a Butterfinger. However, the next camera angle from inside of the helicopter shows one of the soldiers handing the Butterfinger to Dieter, who looks at it as if it were his first time seeing it.
In the air to ground attack, the plane's 2.5" rockets are shown to be dropped like bombs; rockets are fired, not dropped. Even if the rockets in this instance were bombs, it would be rare for them to be dropped all at once.