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.
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.
Character mistake: When Katniss is trying to destroy the supply pile, we see a close up of her drawing back on the her bow. We see she has the arrow to the left of the grip, meaning the fletchings (feathers at the end by the string) have to be facing to the left. Otherwise the fletchings will hit the grip, rip off, and make the arrow unstable in flight and go completely off course. However, the fletchings are are facing to the right and so will hit the grip. Any archer or anyone who is skilled with a bow would know this.
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 Katniss sleeps in the tree for the second time she has a cover over her legs. After camera changes angle the cover is gone.
Continuity mistake: During the reaping, as Katniss fights with the peace keepers to get to Prim, there is an obvious break in the shot. In one shot, she is already pushing the peace keeper on her left off, but in the next shot, she is just beginning to push him.
Continuity mistake: When Katniss meets Cinna, he has 4 earrings in his left ear and 2 in his right, so the last shot (when he says that Katniss "shouldn't be dressed up in some stupid costume") is clearly inverted.
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).