Audio problem: When Katniss kills Marvel with her bow and arrow when she's with Rue, the cannon (which goes off when a tribute dies) doesn't fire. This happens a couple of other times in the movie too. (01:25:25)
Suggested correction: This isn't a mistake. First the cannons never went off immediately as evidence by the fact that after the initial battle when tributes were killed, they don't go off until Katniss got away. Then 6 went off in a row. The people in charge of the games decide when they go off. Plus, after Rue is killed, the audio cuts from all sounds of the arena for dramatic effect. The cannons could have gone off then. Or they could have gone off during the District 11 riot.
Continuity mistake: In the evaluation scene where Katniss shows off her bow and arrow skills, there are 4 arrows total. However, when she leaves, all 4 are gone, and she only shot 3.
Suggested correction: When she comes in, there are 5 arrows. She shoots 3 and when she walks away, you see 2 arrows left.
Factual error: At one point in the film, Katniss passes out after being stung by wasps numerous times. When she asks how long it had been upon awakening, Rue answers, "A couple of days." If she had been out that long, and as a result been unable to drink, she would be in very bad condition, not to mention the fact that she would immediately need to use the bathroom.
Suggested correction: You can help an unconscious person stay hydrated by gently pouring small amounts of water into their mouth. They'll swallow it by reflex.
Continuity mistake: As well as being an audio problem, the cannon sound representing the death of a tribute is not consistent. It goes off shortly after the bloodbath scene and the scene in which Peeta kills a girl. It doesn't go off for any other deaths though, such as when Rue dies.