Continuity mistake: When Ariadne wakes in the Snow Fortress and the floor goes from under her, we can see her gloves fall in to the crack but in a different camera shot of her we can see the gloves are now back near her head again. (02:12:20)
Revealing mistake: When Ariadne is pulling the two huge mirrors close together underneath the bridge with Cobb, watch her when she is closing the second mirror. She steps over something even though there is nothing present for her to step over. There must have been a green screen frame there for her to step over.
Continuity mistake: When they escape from the building in the first dream, the right-hand mirror of the van is broken by the narrow gate. In the following shot when they are driving, the other mirror is broken and the right mirror is suddenly undamaged.
Continuity mistake: In the hotel scene when Ariadne and Arthur are sitting watching Mr Charles walk in to talk to Fischer, we can see she has earrings, but later when Ariadne asks "wait, whose subconscious are we going into?" we can briefly see she has no earrings.
Continuity mistake: When Cobb and Arthur are leaving their hotel room to get on a helicopter on the roof, we can see it's quite dark outside. But in the shot of them on the roof, it's much brighter.
Continuity mistake: At the beginning of the movie, when Cobb and Arthur are on the top of the building about to get into a helicopter to leave, they find Saito in their helicopter. During the dialogue between Saito and Cobb, the window of the helicopter behind Saito is wet and being rained on. But when the camera cuts to Cobb outside the helicopter, it is not raining at all. This happens multiple times in the scene. As the helicopter flies away at the end of the scene, there is no rain.
Deliberate mistake: During the mob scene outside Saito's love nest, the same black Saab is seen getting firebombed twice. It was shot from two different angles, with the two shots played about a minute apart to give the impression of two cars getting bombed. Also, in the first angle it is clear the car has no engine.
Visible crew/equipment: During the zero-gravity fight scene in the hotel room, it is possible to see a crew member's hand briefly resting against the end of the bed when Arthur and the projection are fighting on it.
Continuity mistake: Third dream level, there are six henchmen being pulled by the Hummer snowmobile, and the back right gets shot off (or taken out). A scene a few minutes later, the missing henchman is back, then a few minutes later he is gone again.
Continuity mistake: As the van is in free-fall from the bridge to the water, Arthur's headphones disappear and then reappear between various shots.
Continuity mistake: When Arthur is fighting the projection in the hallway and begins to strangle him using the projections arm, we see his arm is covering his mouth.However in the next shot his arm is around his neck and his mouth is uncovered. (01:48:55)
Continuity mistake: In the second scene, when Cobb is taken to Saito (Old Man), Cobb's totem is kept on the table with the longer end down. But as the PoV changes to Saito's, the totem keeps changing position with the shorter end down. This happens at least four times. (00:01:45)
Continuity mistake: In the scene where Ariadne finds out that the only way Cobb can dream is by being hooked up to the machine. When she first walks in and sees him sleeping on the chair she has a purse over her left arm. But in the next shot, she has no purse on either shoulder and there's no shot showing her putting the purse down. (00:54:20)
Deliberate mistake: The exact same filmed footage of sleeping Arthur is shown in two different scenes inside the van. This repeated slow-motion scene shows his left hand rising and two spherical droplets of water drift towards his right eye. It can be first seen when the van is being chased out of an alley and makes a right turn onto a street. Then it can be seen again soon after the motorcycle rider smashes into the windscreen. Watch for it when the van passes through open gates and makes a right turn. (01:29:30 - 01:38:55)
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: When the train comes barreling down the street in the level 1 dream (on the plane) in the rain, the length changes. In an overhead shot we can see what appears to be three cars (including engine). It is moving quite quickly and should pass them in no time, but Cobb has to back around the train and catch up. It appears as he is backing around that more than three train cars have passed. (01:06:05)
Chosen answer: He bought out the actual airline company. If he'd bought out all the tickets for that specific journey he'd have said "I bought out the flight" or similar. It's a deliberately over the top moment of exuberance to highlight exactly how rich Satio is. I'm afraid that it is your friend who is correct, sorry.
Manky