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).
Continuity mistake: When Katniss and Prim are entering the square, Prim panics and Katniss tries to calm her. During that dialog, Katniss' hands suddenly appear holding Prim's face.
Continuity mistake: In the scene where Katniss is being interviewed by Caesar on stage before the games, her hair is securely up kept in the back. As she is twirling to show off the flames, you notice her hair has come undone a bit and is drooping in the back. By the end of her twirling, her hair has returned to its previous secure up-do. By the end of the interview, her hair is sagging once again in the back. Then, returning backstage with Haymitch and Effie, her hair has returned to being secure and neat.
Continuity mistake: When we first see the large board with each tribute's odds, you can see that Rue's are 60-1 and Thresh's are 10-1 (moving to 11-1). When the view changes, the odds are 8-1 for Thresh (could be) and 7-1 for Rue (no way she has the same odds as Glimmer!). Rue's name also disappears.
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.