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)
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: 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: 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)
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