Revealing mistake: The final scene is filmed in Brant Rock MA, and the weather is blatantly CGI. If you notice almost everyone is bone dry in a supposed driving rain storm. Look especially at the character perched on top of the submarine tower. For contrast note the "pizza delivery" scene where it is raining heavily and everyone involved is soaking wet.
Revealing mistake: During the police chase with Gabriel on his motorcycle, he stops and turns to start shooting at one of the cops. By appearances, Gabriel is using a standard Glock which had a magazine capacity of 15 rounds. He has no extensions on it at all with the handle and magazine visible. Yet he proceeds to fire the gun 33-35 times at the cop car without reloading and in continuous fire. (00:57:55)
Revealing mistake: Fight in the toilet of the Paris nightclub: the presumed Lark rips out the sink's drain and begins assaulting Tom Cruise with it; Walker intervenes holding him, but the nimble Asian does a flip and brutally tosses him to the ground. As Henry Cavill is bent over before being snapped to the floor, on his back, you can definitely see a protective pad through the jacket. (00:31:52)
Revealing mistake: When Evelyn is hanging the clothes after washing them, they are already dry.
Revealing mistake: Normally I wouldn't consider a bad CGI effect to be a mistake, but when Elise finds the hidden keyhole in the wall in the basement, the effect is comical if you pay attention. The way it appears as she scratches is pretty unnatural, and the pieces of paint that fall practically look like cartoon pieces if you pay attention. The shadow of her left hand also looks a little too sharp compared to the rest of her (somewhat softer) shadow, revealing it was likely rotoscopped in some way.
Revealing mistake: When the agent is questioning Fat Freddy after the cop finds him with coke and a gun, she puts a phone up to his face and says "say cheese." She holds the phone up to his face with the screen facing him. You hear the click and beep of the phone taking a picture, but when she turns the phone around, it's still on the locked screen with just the background and a clock. (01:06:45)
Revealing mistake: Eve says they need to make sure nobody gets shot, so she picks up Franklin's pistol and takes out the magazine to store them separately. However in this shot the magazine is completely empty with no bullets anyway. (00:53:40)
Revealing mistake: When Brother Swan goes to blow on the "horn" (which is actually an ocarina), he toots out a few different notes. However his fingers stay completely stationary on the instrument and not moving around on the holes to change the notes. So it would have been just one sound but it plays like 3. (00:29:25)
Revealing mistake: While they're finally on the rapids, the girl blindfold keeps changing position from her neck to her forehead. (01:40:59)
Revealing mistake: Davey at the beginning of the movie is looking at the newspaper he's delivering to Mr. Wayne Mackey. Just from a glance at the page you can tell that something is off, since the article supposedly about a missing boy appears to be written entirely in first person. Upon closer inspection, turns out that it's filler text from chapter IV of Robert Louis Stevenson' s "Treasure Island". (00:01:30)
Revealing mistake: When Kurt and Elisabeth are looking at the painting of the Third Reich caricatures, in the shot focusing on them, a little girl in the background can be seen glancing at the camera. (00:01:45)
Revealing mistake: When Asher is shooting a bolt-action sniper rifle there's no casing ejecting from the rifle as he reloads it with the bolt. (00:48:30 - 00:49:25)
Revealing mistake: After Jess leaned her bicycle against the pole, it slid down onto the ground. In subsequent views of the bicycle to Jess' side, the bicycle appeared to be upright and not what would be expected if it was lying on the ground. The height of the bicycle's seat should have been closer to the chair's arm, not Jess' shoulder. At a different angle before Jess got up, the bicycle was positioned like it was right after it slid onto the ground. (01:04:02 - 01:05:47)
Revealing mistake: When the Wolf King is arriving through the elevator, there's a shot from a distance featuring Jodie Foster that wheels a chair in. You can see in it that the elevator arrow display is not moving; nobody is using them. (00:50:35)
Revealing mistake: When Bearman and the President are running from the Russians, we see some Russian 4x4's doing a hard turn to chase them. In this shot you can see skid marks from previous takes. (01:15:30)
Revealing mistake: After Mel is killed, Scott drives away in a truck that they were just hiding behind during the shoot out. But there is not a single bullet hole or sign of damage to the truck.