Continuity mistake: Cross is holding a normal striker fired (no external hammer) Glock handgun against the head of Ant-Man. In order to save his life, Hope orders the ants to block the firing mechanism of the gun, and they block a suddenly-visible hammer on the Glock. (01:26:00 - 01:27:00)
Continuity mistake: When Cross is on the model rail track, you see Thomas the tank engine fall off the track when he hits Cross. But in the next scene Cross throws him from the track. (01:40:00)
Continuity mistake: When Cross is seen inside Hank's home, he is wearing black gloves, a few moments later, in the same scene you can see that he is not wearing them anymore.
Continuity mistake: When they are going over the plan for the last time at Pym's house a close up of Luis shows his top button undone, then the next close up it's done up with no time to do it.
Continuity mistake: After getting fired from Baskin-Robbins, Scott goes "home" to the Milgrom Hotel. As he approaches, there is a bicycle chained to a parking meter in front of the hotel; it is also visible in the close shot through the gate from inside. In the long inside shot from down the hall as Scott actually enters, the bike is gone.
Continuity mistake: Towards the end while Scott, Paxton and Cassie are eating, the steak on Cassie's plate moves between shots.
Continuity mistake: During the train fight at the end Thomas the Tank Engine is knocked completely off the track and lands on the table, but in the next shot it's lying on the track, where it is picked up and thrown at Ant-Man. Additionally, Yellowjacket is not visible when the train collides with him.
Continuity mistake: When Scott uses the suit for the first time, he is on a tube with a small red towel on it which disappears between shots. Not only this - the amount of food on the plate reduces and then increases during the scene.
Continuity mistake: When Scott escapes from jail with the help of the ants, as he's flying through the trolley car he lands on a newspaper. From the position of the man's thumb, the picture is just a small part of the left side (his thumb lays over about half the width of the picture). When it cuts to the wide shot, the picture now covers more than half the page (width-wise).
Continuity mistake: When Scott wakes up after falling off Anthony, we can see the floor around the bed and there are no ants there. He then looks down and sees the bed is surrounded by ants.
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