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. Twelve are supposed to be dead at that point in the movie.
Continuity mistake: In the shot where Katniss walks up the steps after volunteering to replace Primrose, Effie's fingers are waving her forward, but on the giant screen visible in the background, her hand is still.
Revealing mistake: When Katniss is blown back from the explosion, her stunt person is visible. This can be proven because the stuntperson's skin tone is different and her hair is not in a braid. It is in a ponytail. Wires can also be seen pulling her to give the illusion that she was blown back from the explosion.
Other mistake: We are told that there are a boy and a girl tribute from each of the 12 districts, making a total of 24 tributes. However, in the scene when Katniss is figuring out the Cornucopia stockpile is mined, the camera sweeps round dug-up earth next to all of the launch pedestals - yet only 20 pedestals can be counted. This can also be seen from an aerial shot in the same scene.
Continuity mistake: When Katniss is retrieving the second parachute (the one with the soup), the piece of paper with Haymitch's message changes between shots (the corners are / aren't torn) and they way Katniss is holding it also changes (from below / from the side).
Other mistake: When Katniss retrieves the bow and arrows from Glimmer, there are six arrows in the quiver. She probably recovered the two arrows that Glimmer and Cato shot at her in the tree, bringing the total to eight. Katniss did not recover the two arrows she used to blow up the Careers' supplies, bringing her total down to six. She probably recovered the arrow used to kill Marvel, but did not recover the two arrows she shot at Clove, bringing her total to five. She did not recover the arrow used to kill the muttation, nor did she recover the two arrows used on Cato, meaning that at the end of the Games, she should only have had two arrows remaining. However, at the end, she still had about half a dozen arrows remaining.
Continuity mistake: The tracker jacker nest Katniss is trying to release by sawing off the branch it hangs from, is alternately shown resting on another branch, then hanging freely.
Continuity mistake: In the scene where Peeta is throwing the huge metal ball, you all know that Cato, Marvel and Glimmer are watching. In the 2 last shots where the 3 of the are shown, Cato's stance is shifted. The first shot is zoomed out where you can also see the metal ball, in this shot Cato is standing with his arms hanging and slightly rotated to his right side. You can see him move to the left side, but in the shot directly after he is standing rotated to his left with his arms crossed.
Other mistake: When Katniss, Peeta, and Cato are on top of the Cornucopia (after being chased by the muttations), near the end of the film, Katniss aims an arrow at Cato while having Peeta in a headlock. Katniss has her arrow fletchings on backwards. This would prevent her from shooting straight.
Continuity mistake: In the scene where Katniss uses the remote to change the scene in her bedroom window in the Capitol, her hair starts out stringy (having just been taken out of the braids she wore in the opening ceremony) and changes to full and beautiful and switches positions around her face and shoulders as the scene progresses.