Continuity mistake: Just as President Snow starts to give his speech we see Prim, Katniss and Mrs. Everdeane sat on the sofa. Mrs. Everdeane has her legs crossed in one shot and side by side in the next.
Continuity mistake: When Gale and Katniss are talking atop the hill about how they should have left earlier, Katniss removes her hand from Gale's neck/face. The camera cuts to the other side and her hand is back there.
The old man executed in District 11 was shot in the head from behind. However, when Katniss looks out the window from above there are no blood stains on the floor, nor is there a gunshot wound to the head.