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.
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: 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).
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.