Other mistake: What special "something" does Nick Fury use to pick the Cosmic Cube up at the beginning of the movie? All I saw was that he had on a glove, but in Captain America it was said only people with special abilities could handle it, and even later in the The Avengers when Banner is moving the cube, he uses a gadget and he's the Hulk! Did I miss something?
Suggested correction: Captain America and the Hulk are both more cautious than Fury, and it's revealed in Captain Marvel that Fury knows more about the tesseract than most and had dealt with it before. We know that the cube is just a vessel holding an infinity stone. The danger is what the cube contains. The fact his character decides to risk it based on previous experience isn't a mistake.
Continuity mistake: Once Iron Man finishes with his project underwater, he surfaces and begins flying towards the city. The view from behind shows a very long and noticeable vapor trail coming from his jet boots that stretches far back. But when the shot cuts to being in front of Iron Man and going with him, the vapor trail is much shorter, dissipating quickly, and hardly noticeable. (00:23:30)
Continuity mistake: When Natasha is tied up on the chair talking on the phone, a strand of hair on the keyboard appears/disappears between shots. (00:14:05)
Continuity mistake: Towards the end while the Avengers are on the news, there is a guy spray painting "the Avengers" on a wall. The style of the letters changes between shots.
Continuity mistake: Selvig is carefully moving a cylinder of iridium from a scale to its final location with a metal tongs. The way he holds the tongs changes, when it is highly unlikely that Selvig would change his grip while moving such a delicate substance. Most noticeable are his index and middle fingers. (01:01:20)
Continuity mistake: As Nick Fury and Selvig are talking about the Tesseract, an overview shot is shown where Fury says "I assumed you pulled the plug" and Selvig says "She's an energy source." This shot shows Fury and Selvig in the far background and we can see they are standing even with each other, but in a sudden close-up of the two, Selvig is suddenly standing in front of Fury. (00:03:05)
Continuity mistake: As Nick Fury is telling Agent Hill that he will act as if the world intends to spin on, and to clear out the tech below, the first shot from behind her shows she has her head leaning slightly to the right. It cuts to a frontal view of her and her head is leaning slightly to the left. (00:02:45)
Revealing mistake: Near the end, Captain America is shown riding a motorcycle without a helmet. Although the movement of the background indicates he's traveling at a good speed, his hair doesn't move.
Continuity mistake: After Hawkeye fires an arrow at the Helicarrier and part of it explodes, Bruce and Romanoff are knocked out of the room and land on a lower level. As they land, they are shown to be right next to each other, but when they are shown next, the distance between the two has increased by at least two feet. (01:09:45 - 01:10:25)
