Other mistake: After the Teflon-coated bullet is removed from DeNiro, he states that Sergi was trying to "stamp him." The bullet that hit DeNiro was actually a ricochet that Sergi fired at Jean Reno. DeNiro would have known this as he watched it happen. (01:14:20)
Other mistake: When the arms deal goes wrong by the river in Paris, Larry drives the Audi flat out straight into the tunnel where the bad guys BMW is parked right in the middle, leaving little space to get another car through. Even if he could squeeze the Audi past the other car, there were dead bodies either side that he would have to drive over, as well as crashing into the doors that were left open. This would have done some damage to the Audi at the speed he was going.
Other mistake: At the very end of the final chase, Vincent fires his gun and the BMW wheel was slashed. But Vincent aims his gun to a higher position, not to the position of a car wheel.
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.