Audio problem: Near the start of the movie, Darren Cross is showing the Yellowjacket armour to a group of some visitors. One person, named Frank begins talking with Cross about the armour. There is one shot shown during the talk, with the camera behind Frank's shoulder. In the shot, Frank is heard talking but his jaw is not shown moving along with the line.
Continuity mistake: Scott's stubble changes dramatically in three consecutive scenes - when his boss sacks him it is quite pronounced, but on his way home it is much lighter, and when he enters the apartment it is back to full-on stubble again.
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: Outside, when the tank hits the ground after bursting from the building, where did all the people who were being evacuated go? They were there in the previous shot, and since the tank landed on the path, Hank should have been in front, just behind or even on top of a few.
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