Factual error: Ant-Man is riding carpenter ants after a helicopter in flight. The ants are coming at the helicopter from under it as it rises off the helipad. This wouldn't be possible due to the down force of air from the rotors. (01:30:00)
Factual error: Near the end, Scott Lang inadvertently shrinks to subatomic size, drifting through a kaleidoscopic quantum universe, and we see him reacting to the visual effects. However, at subatomic size, Scott shouldn't be able to "see" anything, because the rods and cones in the human retina can only "see" in a narrow band of light frequencies, and Scott is far, far smaller than the frequency of visible light waves. Additionally, Scott couldn't possibly "hear" his daughter Cassie crying "Where are you, Daddy?" Human hearing is based completely on air vibrations at certain frequencies, and Scott is millions of times smaller than sonic frequencies or even the nearest air molecule.
Factual error: In the scene when The Wasp (Hank's wife) goes subatomic to deactivate a missile, you see the missile flying horizontally in the clouds. That is not possible. First, that missile does not have wings so it simply could not fly horizontally like an airplane. Second, Hank states it's a ICBM (Intercontinental Ballistic Missile). ICBMs have a circular trajectory with apogee at 1200km of altitude (750mi), WAY above the clouds.
Continuity mistake: When Scott and Hope are kissing at the end, Hope has her hands on Scott. When the shot flips to the other side, her hands are down.
Continuity mistake: In the scene when Hank arrives at Pym Tech near the end of the movie, Paxton and his partner are sitting in their car. The left headlight is out. When the two exit the vehicle and go to talk with Hank, Gale steals the car with a working left headlight. Also when Paxton and his partner find their car crashed into a tree, the headlight is still on.
Chosen answer: They could have opened it with a crowbar or a Jaws of Life. (Likely the crowbar, since we didn't hear metal rending).
Captain Defenestrator