Allegiant is supposed to happen moments after the end of Insurgent, but Tris' hair is much longer.
Periodically, land beyond the wall appears to be heavily forested. However, once past the wall, the group starts with a cliff down and then it is completely barren with completely different weather conditions (frequent red rain).
In a scene where Four is talking to Tris, he puts his hand on her throat. But when the camera angle changes to look at Tris talking back his hand is on her shoulder. His hand shifts back and forth during the entire scene.
When Four tells Tris that he found out that he's damaged he is sitting at a table eating. On the table there are two small bowls that look empty throughout the scene, however, when Tris gets up to leave and pulls her hand away from Four's, in the close up shot one bowl is now filled with food, and both bowls are in different positions on the table.
After Tris gets a purification shower and fits into a new outfit, her tattoo is shown on the right side of collarbone, whereas it is originally on the left. This happens during the holographic presentation scene.
The DNA spiral is portrayed as a left handed spiral when it is in fact a right handed one.
When Four and Matthew crash, they crawl out of the wreckage and walk away. In reality, no one could possibly survive a crash that experienced the G forces shown, especially if they were thrown around inside the aircraft during the impact instead of being strapped into a seat.
Nita explains to Four that the left hand controls the drones, yet later in the film Christina controls her drones with her right hand. Four, being right-handed, was wearing the drone control glove on his left hand, which is why Nita told him to use that hand. Christina is left-handed and wore the glove on her right hand.
When the group of 5 are walking in the wasteland, before the armored vehicle is seen jumping over them, you can hear the footsteps of them echoing. This is due to them being on a soundstage. If they were in the outdoors, you wouldn't hear an echo.
The wristband that Four takes when he is beaten up and uses to escape his cell is actually a Samsung Gear Fit smartwatch.
Considering the width of the wall and the proximity of the vehicles to the base of it, there is no possible way that Edgar could have shot Tori at 21:32.
In the first and second parts of the series, Chicago is a bustling city and the buildings are in good condition. In the third film, the bridges and most of the buildings are in ruins, with only a few structures appearing untouched. There is nothing but the wall, whereas in the previous films, fields and forests can be seen. This shocking change is not explained.
When Tris and Christina are going to rescue Four, Tris asks how to use the drones. When Christina tells her that she must use her left hand she can be seen using her right hand to control them.