Other mistake: While Katniss and Johanna are unreeling the wire on the way to the beach, it snags (or is deliberately pulled) behind a rock and Katniss tugs on it till it snaps. The wire was coming off a spool and becoming caught up would have no effect on how the wire unreeled, because the spool would keep on turning regardless. In fact, a taut wire behind her would be what she wanted.
Continuity mistake: When Cesar is introducing the show on the eve of the games, he says "And unfortunately..." and raises a pointed finger above his shoulder level, then says."say good bye to all but one" however the camera has changed angle and his hand should be visible but is not.
Continuity mistake: When the group stumbles across the spile Haymitch had given them, Katniss opens up the container it was in and reads the "Drink up" note inside it. Katniss then places the note back on the container, but by the next shot, as she goes to put the container on the floor, the note has vanished.
Audio problem: When President Snow is having lunch with his granddaughter, Snow asks her when she started wearing her hair differently, and she replies. After Snow finishes this line, his granddaughter's jaw begins to mouth the word movements before she actually begins to speak.