During the District 12 reaping, Effie Trinket is the only character with a microphone. However, after the female tribute has been chosen, Katniss and Primrose's voices can be heard amplified and echoed as if they were using microphones as well, even though neither are near the microphone. This is only in some shots, and the echoes come and go.
When Peeta throws the metal ball at the spears, the career tributes (Cato, Marvel and Clove) are laughing at Peeta before he throws the ball. After Peeta has thrown it, Clove has gone and Glimmer is in her place.
When the 12 chariots are parading to the final stopping spot, the fans are throwing flowers and all kinds of things on the road that they ride in on. When they show the overhead view and the last chariots pull up there is not one item on the roadway.
During The Reaping, in the wide shot when the Mayor and his affiliates are being introduced, there is only a microphone and the chairs on the stage. The Reaping Balls do not appear until Effie draws the names.
When wounded Katniss is on the tree and receives a parachute, she takes off the lid of the can with the medicine and places it underneath it (the can). In the following scene she's holding the lid on the side of the can.
When Katniss is driven from the tree by the fire, she unties her rope and jumps down the tree apparently without putting the rope back in her bag, but the following night, while hiding on a tree from the others who camp beneath her, she has tied herself to the tree again with the same rope.
When Effie Trinket is shown from behind walking to the bowl to draw the girl tribute, she has a lot of hair on her neck. Then, when she is shown from behind going to meet Katniss, she has just a few strands of hair there.
When the shot of the pre-Games "tribute scoreboard" switches from a close-up to a wide shot of the betting area, the board has changed significantly; the images of the Tributes are gone and the odds for each of them have changed. Rue's odds, for example, instantly change from a dire 60-1 to a quite impressive 7-1 chance of winning.
In the 'Reaping' scene when Katniss is seen yelling 'I volunteer' the camera shows her ducking under the Peacekeeper's arms, when the camera once again returns back to her she's back up straining against the Peacekeeper's arms.
After entering her private training session in front of the Gamemakers, Katniss Everdeen picks up a bow and draws it. In the side shot, she removes her index finger of her bow hand from the top of the arrow's shaft while drawing the bow. When the camera switches to over her right shoulder, her index finger is still over the top of the arrow and Katniss only removes it after she has fully drawn the bow.
During the speech from an instructor before the tributes commence their training, Glimmer can be seen to have a pimple on her right cheek, near her chin. This is gone when she is on with Caesar Flickerman, but it could have been covered with makeup. When Katniss is chased up a tree, Glimmer can be seen without the pimple on her cheek, but she has one on her throat, right under her chin, where she didn't have one before. Then, when she laughs at Cato by the campfire, she has a pimple on her right cheek again.
When Katniss is seeing images on the window of her penthouse room, in the forest image, when her face is focused, there is hair in front of her left eye. But after shifting to the forest image and then shifting back to her face, there is no hair in front of her left eye.
When Peeta throws the metal ball at the rack of spears, the District 1 & 2 representatives can be seen in the background with their arms hanging loose. Immediately after that, they are shown with their hands folded together.
During the review by Caesar and Claudius after the initial bloodbath at the Cornucopia, behind them are images of the fallen tributes and their times of death. Some of the times shown are impossibly low, including several tributes shown to have lasted only a fraction of a second, not long enough to have even stepped off of their platforms.
You can see Gale standing outside the doorway waiting for his cue to come in to say his goodbye to Katniss. After her mother and sister leave, she tries the door and opens it a bit and then closes it. As soon as she closes it Gale opens it. You can see Gale standing there when she opens the door.
After Katniss volunteers for Prim, it shows the crowd putting three fingers over their lips and kissing it as a sign of respect. You can clearly see a man in the crowd wearing black with a camera. This is often mistaken as a goof but remember that the 'Reaping' is being televised across Panem.
Katniss has an hallucination in which Caesar is making a comment about the effects of tracker jacker venom. Caesar made this comment minutes earlier on television, same attire, same words, so this hallucination is presented as a flashback. However Katniss did not have the opportunity to watch such comment.
When the game-makers start the fire to force Katniss back toward the tributes, the video of Katniss that the game-makers are watching, as she is running away from the fire, shows video being shot directly in front of her and following her behind her, but there is no camera-person or drone following her around the area to make this possible. If the cameras in the trees were to catch her running, they wouldn't be shaky and keeping up with her while she runs.
When Katniss draws her bow to deliver the coup de grâce to Cato, she initially aims downward as would be expected. But in the next shot, her aim changes to slightly upward. She releases the arrow in a path that would clearly fly far over him.
As Katniss prepares to destroy the stockpile of goods at Cornucopia, Fox Face comes in, dancing her way across the mines, and grabs some food - then simply runs off in a straight line, as though only one side of the pyramid had been mined.
After Katniss has destroyed the stockpile at Cornucopia, she runs back into the forest and stops to whistle to the mockingjay and signal Rue. In the wide shot you can very clearly see a blue marker for where she needed to stop.