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.
Audio problem: When one of the computer operators resumed playing Galaga, the sound effect heard is for an enemy ship attempting to capture the player's ship, but what's shown on screen is normal gameplay.
Audio problem: When the alien cuts Boris's shackles they hit the floor and make a metallic sound, yet when the chest armour falls it sounds like the foam object it really is made of. (00:03:40)
Audio problem: When Joe is telling Old Joe that he'll never meet his wife in the future to prevent her death, a shot from behind Joe is shown, where he says "she'll be safe", but his jaw is never shown moving along with the line. (00:48:15)