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 throws the knife at Tris, he cuts her right ear. When Tris goes to confront him about this, the wound is significantly smaller. Then, back at the dormitories, the wound is back to normal size. However, all three times, the blood is smeared in a different way.
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.
When Tris wakes up after her fight with Peter, she has a large dark bruise on her left cheekbone. When she stares at Eric on the Train, the bruise is gone. Though the next four scenes take place the same night, the bruise would appear and disappear at random.
(at around 25 mins) When the group first jumps from the train and the camera shows "Tris" after landing, she has bloody knuckles on her left hand. Seconds before and the following scenes neither of her hands have any injuries, most visible being when she jumps from the rooftop down into the netting.
Right after Tris' shoots Will, when they run down the alley, Tris looks down and sees him dead, plus another body lying in the alley. When they get to the end of the alley, the camera pans back down the alley and the bodies are gone.
When they are first eating in the "Lunchroom" the container holding the hamburgers is full, but once the camera goes to Max then back to Tris, Christina, Will and Al, the hamburger container is nearly empty.
Four takes the initiates to the wall on the train. When the train stops, the initiates exit the train and we can see the landscape and the wall through the train window. A bush is visible and we can see rust stains on the wall. When the camera raises over the top of the train to show the initiates walking toward the wall the bush is not there and the stains on the wall are in different places.
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.
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.
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.
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.