Revealing mistake: When we see the new recruits at boot camp, they are wearing M1 Helmets. But if you look closely, they have rivets through the sides of each helmet where the chinstrap bales would be. In reality, the M1 helmet chinstrap bales were and continued to be welded onto the shell of the helmet. This indicates the helmets in the film are probably plastic replicas with the bales being riveted in place.
Continuity mistake: When the Howling Commandos break through the windows of the last HYDRA base, first Captain America's on his knees, then when they start shooting he falls down, then right after he's standing up and tosses a HYDRA soldier. (01:35:11)
Continuity mistake: Colonel Phillips walks into the cell that holds Dr. Zola, while carrying a dinner tray. When he puts it on the table the salt and pepper shakers and the glass of milk are on Colonel Phillips' side of the table. In the next shot you can see Colonel Phillips turning the tray around to Dr. Zola. After he refuses the food and Colonel Philips makes a snappy remark about cyanide, Colonel Philips turns the tray back, so the shakers are on his side. But then when he starts eating they are on Dr. Zola's side again. He does move the glass of milk with his right hand and grabs the knife and fork with his left, making it impossible for him to have moved the shakers. (01:26:00 - 01:26:40)
Continuity mistake: During the taxi chase scene, the license plate RY*281F on the cab starts out attached above the single taillight on the left of the vehicle. After Peggy shoots the windshield and she is tackled by Steve, the license plate switches to the opposite side of the vehicle as do the gas cap and a single bullet hole in the rear window. There are several more side swaps like this before the cab crashes.
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.