When Katniss delivers her speech in District 2, she refers to Cato killing Thresh in the 74th Hunger Games. This is a holdover from the books. In the first movie The Hunger Games, Thresh was killed by the mutts, not Cato.
When Katniss talks to Boggs alone out in the square, the shot goes back and forth from showing her face to showing Boggs'. Katniss's hair moves from on top of her hood to inside of her hood between shots.
The color contact lenses Julianne Moore wears for her role as President Alma Coin are clearly visible during a conversation with Plutarch Heavensbee, when they are looking at the screen after the arrival of Katniss in the Capitol.
After Finnick's wedding, when Katniss arrives to the hangar, there are two men walking in the background wearing safety vests. After a few steps, their movement freezes, and when Katniss lifts the elevator's grille, they completely disappear behind her arm.
The goof items below may give away important plot points.
Katniss and Haymitch have a conversation near the end of the film. In this scene, Katniss' costume has a large brass slider on its zipper in tight closeups, but the zipper has no slider in the wider shots.
When Katniss leads the procession down the arena to Snow's execution, two lines of Taiko drummers play a beat; however, the drums shown on screen are timpani / kettle drums, which have a completely different sound to Taiko drums. As seen in a close-up, the timpani have a tuning gauge, implying that they are a pitched instrument. Taiko drums are non-pitched.