(at around 39 mins) After the raid on a sense offender's hideout, Preston takes off his gloves and touches a wall, during which he finds a bullet hole which reveals a stream of light coming through, hinting a hidden room on the other side. However, when he enters this room, no lights are on and it is pitch black.
As the clerics raid the sense offenders' hide out, Preston removes his gloves and drops them. A few shots later he takes them off again, and when he gets home he is once again seen taking off his gloves to take the prozium.
(at around 1h 4 mins) The condition of the picture of Errol and Mary changes from the interrogation room to the scene of Preston at his desk. When Preston shows the picture to Mary it's wrinkled and creased, but one scene later the picture is in a like new condition.
(at around 48 mins) When Preston takes the Dog out to the Nether, he uses his keys to open the trunk and we hear the jingle, but when he gets back in the car, the keys are in the ignition still. (when he gets back out of the car he takes his keys and uses them to open the trunk)
(at around 15 mins) The William Butler Yeats book that Errol keeps is larger and much thicker when he is reading it in the Nethers, compared to when we see it in the car.
(at around 33 mins) It is impossible to see both the sun and a solar rainbow. In order to see a rainbow formed by the sun, a person must be standing with his/her back to the sun.
(at around 6 mins) When they pull the Mona Lisa out from under the floor toward the end of the opening scene, a canvas stretched onto a frame is shown but the actual Mona Lisa is painted on a poplar wood panel.
(at around 6 mins) When they discover the Mona Lisa painting under the floorboard it is about 2.3 feet by 3 feet, where as the real Mona Lisa is 21 inches by 30 inches.
When the painting of the Mona Lisa is taken from under the floorboards and authenticated, it is obviously a canvas painting attached to a frame with corner wedges. However, the Mona Lisa was painted directly on wood, so would not need a frame and stretchers.
(at around 7 mins) The art is slow-burning after sustained point-blank blast from a flame thrower.
(at around 21 mins) During the flashback to Viviana Preston's arrest, when John twists the soldier's wrist to take his weapon the gun is an AR-15/M-16, but it then appears to instantly change to a Beretta AR-70 as he holds it on another guard - actually, this is not a continuity error; Preston first disarms a guard of his AR-15 type rifle (by breaking his fingers), then uses that rifle to deflect the weapon of another guard, whose AR-70 he grabs and turns on its owner (it's not possible to see which kind of rifle he uses during the lightning-quick deflect maneuver).
Avoiding or destroying anything that might provoke a forbidden emotion in their citizens, the authorities wouldn't needlessly risk provoking emotion by executing Preston's wife in front of him.
(at around 1h 5 mins) In a repressive society where all feelings and emotions are illegal and suppressed by drugs, where fashion is functionally drab and beauty is meaningless, Mary still feels she needs to keep her legs and armpits shaved.
(at around 59 mins) In the pistol whipping sequence, two sets of spikes come out of the magazines. When you see Preston's pistol in slow motion about to hit a guards faceplate, there are no spikes present. Also you can clearly see that it is a stuntman in the reflection of the visor.
(at around 59 mins) During the pistol whipping scene, as Preston breaks through the visors of the crash helmets of the guards, a second screen is visible protecting the actors eyes from broken glass.
(at around 1h 35 mins) In the katana fight Preston jabs into one of the men, and it's clearly visible the sword misses the torso, and the actor's actually holding it between his arm and against his chest. In normal playback the move looks nevertheless convincing.
(at around 2 mins) In the opening sequence when the policemen run around the side of the car, the rear window is smashed before the criminals start shooting.
(at around 5 mins) At the end of the night time "gun kata" shootout with the sweepers, Preston's pistols' hammers are not cocked as they would be after firing.
(at around 7 mins) If art is forbidden due to the emotions it provokes, then the authenticity of the Mona Lisa painting is irrelevant. A copy would look like the original, resulting in the same emotional reaction.
(at around 5 mins) In the early shootout in the darkened room, there is unrealistically very little blood spilled.
(at around 44 mins) When the dogs are being executed, the soldier carrying out the executions is holding a Walther WA2000 sniper rifle, but there is the sound of a pump-action shotgun preceding each shot. The soldier carrying the weapon is not seen "pumping" the weapon.
Brandt shows clear anger all throughout his quest to arrest Preston, yet no one questions it.
(at around 22 mins) The arrest of Preston's wife Viviana happened four years before the events of the movie, but nobody is visibly younger in the flashback. While this is possible for adults like Preston, his son and especially his daughter would have grown a lot since then.
A weapons analysis when Brandt arrests Preston for sense offense shows that it was Brandt's firearm that was used in the slaughter of the patrol in the Nethers (when Preston attempts to release the puppy); however, the scene in which Preston slaughters the patrol happens approximately 12 minutes before the scene in the film in which he switches guns with the oblivious Brandt. Preston's line at the supposed moment of the firearm switch is referenced during the arrest scene when the "switch" is revealed to the audience, confirming that it is the time at which the "switch" is considered to have happened; however, if this is the case, Preston could not possibly have had Brandt's gun when he was confronted by the patrol in the Nethers. There is the auxiliary issue that Preston used two pistols in his slaughter of the patrols, meaning that at least one of the guns should still have been matched to Preston.
If Prozium can block emotions in a human mind, it's pointless to outlaw anything that provokes emotions, like art. The medicine would make people immune to this effect.
In the final showdown in Father's office, at least two swordsmen in gray would have been visible for Preston behind the pillars before revealing themselves, as he just walked past those pillars.
(at around 1h 23 mins) After the execution of Mary O'Brien just before John Preston's kneeling and crying, as he turns toward the building, you can see an extra who is walking down the stairs, smirking.