Revealing mistake: In the scene and shot where Arthur explains how to create the looping architecture. On the staircase reveal - as the camera comes to a rest at the end of the "crane down" the entire stair case wobbles at the end of the shot.
Visible crew/equipment: Right before Cobb and Arthur go to the roof to find Saito having Nash in the Helicopter, Cobb and Arthur are in the Hotel Room with windows in the background. In the reflection of the windows, you can easily see the camera and the microphone.
Continuity mistake: In the second layer of the dream, when Ariadne and Arthur are sitting together, Ariadne's hair changes between shots. At some times, her updo is tied on top of her head, and sometimes, it is a bun at the back. It looks as if the hair is completely opened and tied again in a different way between shots. It must be because of the shots being recorded at different times.
Revealing mistake: When Arthur is gathering everything together in zero gravity for his improvised kick, there are several times when you can see the actors' harnesses. Most notably in the seat of Arthur's pants when he grabs the first charge and the backpack out of the air.
Revealing mistake: When Arthur is fighting the two projections in the hotel hallway and the hallway tilts, Arthur grabs hold of and hangs on the right wall with the ceiling to his right. The following scene shows him running on the opposite wall with the ceiling to his left.
Continuity mistake: During the shifting gravity scene in the hotel room, Arthur rolls off the bed, catches the gun, and shoots the projection. As they slide towards the door, Arthur is curled up and facing away from the projection. But in the next shot, when we see them close up, Arthur is facing toward the projection and is no longer curled up.
Continuity mistake: When Ariadne is learning how to make/change terrain, she shifts gravity and makes buildings touch the top of other buildings. However, if you look in the windows of the black hatchback or any other car, you can see sky and clouds visible.
Continuity mistake: In the beginning, after Nash dumps Cobb into the tub, Saito grabs Nash from behind, hits him, and then turns around and points his gun at Arthur. Nash is dry. But, in the next shot, Cobb jumps out of the tub and wrestles Saito to the ground. Before Cobb grabs Saito, it is shown that Nash is now soaked.
Continuity mistake: Just before the shifting gravity, Arthur walks out of the room and begins walking down the hallway. As we see him from behind, the elevator door opens and a projection is revealed. But, when the elevator doors are opening, Arthur slows down and just before we see him from the front view shot, his bead begins to tilt down. Then in the front view shot, he slows and tilts his head down again to avoid the projections contact.
Character mistake: In the final scene Cobb's children class him "daddy!" but Cobb's son also calls him "Leo!"
Factual error: When Cobb arrives at Los Angeles International Airport and is going through immigration, the officer stamps his passport with a black stamp. All passport stamps in the United States are universally the same with a blue oval and pink letters marking the date in the center. Plus the fact that US citizens don't get their passports stamped when they return to the country.
Character mistake: On the Shinkansen train, Cobb says, "I'm getting off in Kyoto." Not exactly wrong, but a moment afterwards they are in Tokyo and you see the Tokyo skyline.
Suggested correction: Yes. He gets off at Kyoto and says "every man for himself." Perhaps this stage of the plan was for him and Arthur to split up to avoid a tail (we do see later that he is being tailed). But regardless of the reason, we see that it is daylight when he leaves the group to get off at Kyoto. Plenty of time for him to be in Tokyo by nightfall.
Audio problem: In the dream-café Cobb talks to Ariadne right before telling her that it's all a dream, but from a side angle the mouth doesn't match the sound coming out, which obviously belongs to the front angles.
Continuity mistake: In the dream-café Ariadne raises her arm to scratch her head, but in the next angle the hand is down.
Continuity mistake: In the café, Ariadne lifts her cup to take a drink and in the very next shot she is putting the cup back down.
Revealing mistake: When the track-Humvee gets blown up, there is a full second delay between the explosion and the Humvee getting flipped.
Continuity mistake: In the scene where Fischer is talking to Browning by his father's bed, in one shot, Fischer changes from looking straight at Browning to looking down at the ground.
Continuity mistake: When Cobb tells Ariadne to draw a maze, she turns her head to the left. A frame later the head is up and she is turning it again.
Continuity mistake: When Cobb hands Fischer the gun in the bathroom, the gun switches hands for one shot.
Continuity mistake: When Adriadne and Cobb sit down, a newspaper stand explodes, but in the next shot it's still standing.