Other mistake: When Nicolas Cage is chasing Sean Connery in the yellow Ferrari, someone already mentioned that the windshield breaks more than once and in the next shot it's in perfect condition again, well I say forget even that. When Cage drives onto the sidewalk and crashes into the meters, the windshield should have been completely destroyed, not cracked. And the same goes for the hood of the car, which is in perfect condition in the next shot.
Other mistake: When Cage throws up in the lavatory, the sink is empty before and after.
Other mistake: When the SEAL team is onboard "Raider one" the pilot says "we're going dark" and SEAL commander gives them order to turn nightvision on. However, when camera shows the chopper from outside, there is a beacon light flashing in its tail. Trained Navy SEALS would never overlook this detail under any circumstances.
Answer: He led them to believe he needed it to break in.