Factual error: In the space shuttle reentry, the space shuttle should enter at about a 45 degree angle, not the extremely low angle they were using. The vertical speed was also wrong, as in both of those mistakes the space shuttle would have burned.
Visible crew/equipment: At the line another "24 hours to the border, assuming we survive" just after the initial penetration into the other side of the crust of the earth, the studio lighting is on full view outside the window of Stanley Tucci.
Factual error: When "Beck" and Commander Iverson are getting ready to re-enter the Earth's atmosphere, a brief shot of his space suit flight badge indicates that he is an Air Force senior airman pilot. However Commander Iverson is a Navy pilot in the astronaut program, and Navy pilots have two totally different styles of flight insignia. Notice how his flight badges differ to the correct ones later in the movie.
Continuity mistake: When Beck is waiting to speak to the General about the hearing it's the middle of the day but when she leaves the building minutes later to see what everyone is talking about outside it's suddenly nighttime.
Continuity mistake: When Virgil gets stuck in the giant geode and the crystal jams the 'impeller', the crystal changes position after few shots.
Continuity mistake: When the radiation hits San Francisco, the General tells Rat to bring up the power grid and you see Stickley leaning on Rat's chair. The camera angle changes and Stickley is no longer leaning on the chair. The camera angle changes again and she's leaning on the chair. She's even seen leaning on the chair with one arm on Rat's left side during a closeup and then the arm behind his head with a wide view. (01:31:47)
Continuity mistake: When Josh and Serge are at the bar talking about how Dr. Zimsky tried to give Josh his autograph, Serge makes the comment and then puts the napkin, which is in his left hand, near his mouth. The camera angle changes and the napkin is no longer near his mouth and it's in his right hand which he's now using to wipe his left hand. (00:22:05)
Answer: To put it simply: NASA's got all the technology and the people trained to use it, and the military is involved in every government project, not just acts of war. Also, the military has a vast and efficient logistics system making it possible to bring the major pieces of equipment together in the short amount of time available.
Phixius ★