Other mistake: The Brigadier says UNIT HQ is 'a Top Secret establishment'. It is, in fact, so secret that it has a large sign outside informing the world not only of its function, but also the name of the commanding officer.
Other mistake: Mace's chest camera sends images from impossible angles - including several that include Mace himself. At the end, his superiors watch him from a camera that's obviously mounted in a tree and not on his person. Yet when Mace smashes his chest camera, the transmission goes dead anyway. (00:48:00)