Continuity mistake: As the hand creature busts the shackles off Boris' legs in Lunar Max, you can see the bottoms of his pants over his metal prison boots. There are only a few folds and wrinkles over his left foot, and the pants over right foot are hardly wrinkled at all, or affected as the creature climbs up his right leg. But only a couple of seconds later, we see another shot of Boris' feet as the creature breaks off the metal sleeve of his arm, and suddenly his pants legs are very wrinkled. Boris was standing perfectly still the entire time. Boris' legs are also suddenly closer together. (00:03:35)
Factual error: Before receiving the North American P-51D Mustangs, the Red Tail squadron was using the Curtiss P-40E Warhawk. The movie shows the Warhawks being able to keep up with the German Bf 109 G-6s quite easily, fighting on even terms. In reality, the Bf 109 G-6 could easily outperform the Warhawk, being able to easily outrun and out-turn the Warhawk. Still, the Bf 109s are no match for the Warhawks.
Factual error: After the Missouri knocks the shield down, the admiral orders all aircraft launched, but the flight deck is shown in sailing transport mode, not flight readiness. Would have taken an hour or more to clear the deck and launch.
Other mistake: The video stream displayed in the night sky showing which tributes have died after the first day does not add up correctly. They display in district order. We see the start, the girl from three (so the boy is still alive), and the boy from four with no breaks. Then they break away to show Katniss and the control room, after which they continuously show the boy and girl from seven, the boy from eight (so the girl is still alive), the girl from nine (so the boy is still alive), and then fade to the end. We know that Foxface, the girl from five, dies later in the movie. Even if we assume that during the portion not shown, the girl from four, the boy from five, and both tributes from six are dead, that's only a total of ten. Thirteen are supposed to be dead at that point in the movie. (01:16:20)
Factual error: The type of surgery shown made by the machine transversely cuts the rectus abdominis muscles. Besides not being a standard surgical incision in order to "remove a foreign body" as stated, it seriously damages important muscles of the abdominal wall making any immediate active mobilization of the trunk virtually impossible, even under strong analgesia.
Plot hole: During the scene where Merida gives her speech on "breaking tradition", her mother, as a bear, moves silently behind the majority of the crowd, so they don't see her. Fair enough. However, Merida and her father's clan are all looking in the same general direction (towards the crowd) while she's speaking - how does no one from Merida's clan see a bear moving at the back of the room?
Continuity mistake: Bryan is cornered in an Istanbul alley and engages in fierce hand-to-hand combat with Albanian gangsters. Bryan takes one of the gangsters hostage, holds a gun to the gangster's face and threatens to kill him. Another gangster doesn't even hesitate to shoot Bryan's hostage in the back multiple times, and the guy drops down dead at Bryan's feet. Bryan is frozen on the spot. Camera cuts to another Albanian gangster entering the alley, holding Lenore hostage. Camera cuts to close up of Bryan, who quickly calls his daughter Kim to warn her. Camera cuts back to a full view of the alley, and the dead guy at Bryan's feet has completely vanished.