Factual error: When the French President uses his nuclear trigger, the device he uses has a button labelled 'bras'. Bras is the French for 'arm' as in arms and legs. Presumably someone was supposed to look up the word for 'arm' as in arm a weapon.
Factual error: You can't launch a tungsten (or any other heavy object) at a terrestrial target such as a city and create as much destruction as a nuclear weapon. The energy that creates the destruction is kinetic energy: Mass x Velocity^2. A Tungsten rod as depicted would need to travel at around ~400,000mph to create that destruction. That impact would also create an EMP disabling half the planet. (large/energetic asteroid impacts create EMPs and radioactivity too).
Plot hole: How do you construct and launch into orbit 7 Zeus platforms in complete secrecy? Based on the scenes depicting them, you also couldn't launch the Zeus in a single piece... so probably it would be dozens of launches too. You couldn't hide this from a budget. It would take years to get it over the line. Zartan only replaced the president a short time ago... it goes beyond impossible. (01:25:00 - 01:27:00)
Factual error: The shots of Fort Sumter in Charleston, SC show a bridge nearby. Fort Sumter is far out in the harbor - there are no bridges anywhere nearby. Fort Sumter is accessible only by boat, and there is no footbridge crossing a moat. (01:19:00)
Chosen answer: I believe three are named as Grunt, Clutch and Tunnel Rat in the script and credits.