Factual error: During the night chase scene through London streets, a subterranean vehicle emerges from the ground. The drill head is turning in the wrong direction and would be ineffective for the same reasons as turning a screw in the wrong direction.
Factual error: While hiding in the arctic cave, one of the minions eats a banana. However, the minions are supposed to have been trapped there for many years and edible bananas are restricted to tropical or near-tropical regions, roughly the area between latitudes 30°N and 30°S. It would not be possible for them to have bananas.