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 Katniss says "that's the first deer I've seen in a year" towards the end of the line you can see her mouth doesn't move. (00:05:50)
Audio problem: When Katniss offers to show off her flames, Caesar laughs and asks "what do you think folks?" however, his mouth, (which is facing away but his jaw is visible), doesn't move. (00:53:00)