Continuity mistake: John's staff sergeant military shoulder epaulet markings become upside down in the scene when he and Savannah are having dinner at her house when he comes to see her after his dad died. In a later shot shortly after, they are correct.
Other mistake: Before the battle, the leader of the waterbenders says that he will have everyone extinguish as many sources of fire as possible. When the firebenders come up from the ground at the start of the battle, all of the torches lighting the city are lit.
Plot hole: There is no way Freddy could know where to find Al Rawi to gun him down. After a lengthy, chaotic chase through Baghdad, Al Rawi is about to be captured by Miller, and Freddie simply shows up. This makes no sense at all.
Continuity mistake: When Ellie & Fiona are breaking into the garage to steal the gas tanker truck, Fiona's hands are by her side. The camera angle changes, and her right hand is up, holding her rifle strap.