Revealing mistake: At the start of the chase, the Mercedes slides around a bit, and it is comically obvious that the tire smoke has been poorly painted onto the scene. (00:45:15)
Revealing mistake: In the rink, only a few shots after Natasha Kirilova is introduced, the camera pans across the crowd where Sam and Vincent are sitting and you can see that the upper half of the crowd are all cardboard cutout people.
Revealing mistake: During the final chase scene with the BMW and the Peugeot. Just as they go down into the first tunnel, they cut in front of a car transporter forcing it to brake hard. A car on top of it then flips forward onto the road. If you look at the ramp as the car tips up, you can see a mechanical arm/rod lift it up to make it fall off.
Revealing mistake: In the final chase a car gets spun around and hit by a lorry - the car driver is an obvious dummy.
Revealing mistake: Obvious studio shot when the BMW starts to flip at the end.
Chosen answer: It is true that it doesn't affect the plot. However Spence's (Bean's) failure can be contrasted with the professionalism of the main characters. Also it raises the possibility that whoever hired them isn't taking necessary precautions in planning and hiring. Earlier we heard Sam (De Niro) ask Vincent (Reno) if he was "labour or management" which suggests a theme of professional operators getting their hands dirty while their bosses play politics.