Continuity mistake: When Agent Carter shoots Rogers while he is holding his shield, she picks up a M1911A1 pistol. When she does, it has the hammer down, but it cuts straight from her reaching for it to her shooting it, without her cocking the hammer first, which needs to be done since the pistol is single action only.
Suggested correction: The Colt M1911A1 is a single-action semi-automatic pistol, meaning when the pistol has a bullet in it's chamber by cycling the slide you don't need to manually pull the hammer down to fire. It doesn't work like a single action revolver where you have to pull down the hammer manually each time to fire. You could, for a shorter trigger, but you don't have to because of the slide. In other words, the pistol Agent Carter picked up was loaded with a bullet in the chamber and ready to fire without having to manually pull down the hammer.
The correction is incorrect. A 1911 pistol is hammer fired, meaning the hammer must fall on the firing pin in order for it to fire. The hammer is down in the scene, which meant the pistol would not have fired. However, since the hammer not being down is only visible when using slow motion (the hammer is obscured by Agent Carter's hand in most of the shot), the original mistake is invalid.