Tris' ear is cut and left bleeding by knife thrown by Four. However, when she meets Jeanine shortly afterwards there is no mark or scar but the cut reappears later when she fights Peter.
When Tris and Four are climbing the ferris wheel, Tris's foot goes through one of the rungs on the ladder. Yet when they begin climbing again after Four steadies her, there are no rungs missing.
When Four throws the first knife, he has three more knives in his left hand. When he is about to throw the second one, the knives in his other hand disappear.
When Jeanine speaks to Tris in the Dauntless passage, Tris' hair covers the cut on her ear. When the camera switches to the close-up, the wound is revealed and her hair is behind her ear. This switches throughout the scene.
After Four reveals his back tattoo to Tris and they kiss, there is a wound on a knuckle of Tris's left hand. The hand is then hidden briefly while she puts her arm around his neck. In the following shot her knuckles are visible again and the wound has disappeared.
During the choosing ceremony the first Dauntless to choose is a boy named Jeffrey Yates. Later on when the score board is shown, there is no one named Jeffrey on the board, however he could have chosen to change his name like Tris.
Early on when we see Dauntless jump off the train and roll down the hill, some of the dauntless vanish into thin air after hitting the ground and rolling. They never make it off screen indicating the point where the blue/green screen ended.
When the hand of Jeanine Matthews is pinned to the computer screen by a knife thrown by Tris, you can see the handle of the knife, which must be adhered to the back of actress Kate Winslet's hand, wobble up and down slightly as she screams.
Seconds before the train approaches the platform to take the new Dauntless to the Dauntless compound after the Choosing Ceremony, the buildings on the right wobbled briefly, indicating that the buildings were actually a set backdrop, thin enough to yield to the train's wake.
In the initiation scene everybody cuts their hands with a knife and spills blood in the bowl of chosen fraction. When Tris' turn comes the bowls must be full of blood drops. But they are not.
Early in the film, the Dauntless faction are coming back from the Choosing Ceremony and jump off the train onto the top of a building. When they land they roll forwards but not sideways, indicating that they were actually jumping from a stationary, rather than moving, start point.
When Tris is viewing the bowls in the choosing ceremony, the Erudite bowl has fresh water, despite the fact that others chose Erudite and they did not change the water. The water should be red.
No explanation is ever offered for such a destitute society which is dependent on small turbines for electricity being able to build & operate a gigantic fence (which is so large that people can walk through it), develop magical drugs, scan brains and display hallucinations on TVs in real time, power an elevated train system with cars that don't seem to stop at stations (they only stop when it's convenient for the plot) or carry any passengers other than Dauntless, produce fuel for giant trucks to be used as patrol cars, burn perfectly good clothing, or produce uniforms for all the citizens.
As the camera pans up the fence and looks across Chicago, it's clear that there is no fence on the far side of the city.
When Four is injected with the suggestive serum and Tris begs Four to recognize her, she points the gun to her own head, and then he finally snaps out of it, but calls her " Trin", not Tris.
During the body surfing in the cafeteria scene, one of the boys that walks past the shot to pick up one of the characters is used again later on as an Erudite guard after Tris goes to see Caleb and gets stopped on her way out.
While Shailene Woodley might not know how to use a kitchen knife when preparing food, Tris certainly would. She is not cutting the carrots using the kind of efficient stroke that an experienced cook would, but she is not using the right kind of knife.