Factual error: In the scene in Stuttgart, we see a "reserved parking" sign written as "Reservierten Parken". First of all, this is grammatically wrong - if used at all, it should be "Reserviertes Parken". But you wouldn't find a sign in Germany saying that. They say "Reservierter Parkplatz".
Continuity mistake: Throughout the film, Tony Stark's chest ring can be seen glowing through his shirt except for two occasions when it's suddenly off - after Loki escapes from the helicarrier, and when Loki and Tony Stark are talking in Stark tower, even when he's wearing the same shirt. (01:35:30)
Continuity mistake: When Hawkeye is breaking onto the Helicarrier, he and some snipers break down a duct cover and enter. When the cover lands on the floor, it is resting away from some pipes with some slats missing. As soon as Hawkeye enters the duct, the cover is now resting against the pipes, and the slats have reappeared. (01:10:35)
Continuity mistake: When the plane lands on the aircraft carrier, it is about to land on a yellow mark on the ground. The angle cuts and it's now landing in front of it. Then from the aerial angle it lands in the middle of both lanes, but a frame later it's on the right lane. Finally, the landing signal officer swaps from standing in front of the plane waving his arms, to several meters behind standing still. (00:31:45)
Factual error: The Mark 7 takes 9 seconds to assemble - give or take. Judging by the view of the Chrysler Building, Stark Tower is about 300 meters high. Even if you discount the time it takes for the suit to catch up with Tony, 9 seconds is too long, he would hit the ground before the suit would fully assemble. (01:41:35)
Continuity mistake: When Tony goes after the nuke, there is a huge cut visible above his right eyebrow (or viewer's left). Later on after his face mask is removed, his right eyebrow is completely visible in the shot, even with the helmet in the way, and the cut is nowhere in sight. (02:00:00 - 02:03:00)
Continuity mistake: During the big battle against the Chitauri, Captain America is zapped with a blaster bolt. When Thor helps him to his feet we can see a significant amount of damage done to his suit, just below the star on the right hand side. But later on after Iron Man destroys the Chitauri ship with the nuke, the damage is completely gone. (01:59:25 - 02:02:40)
Continuity mistake: When Steve and Coulson land on the Helicarrier, you can see two wings on the edge of the Quinjet they were in and they are both closed up. Next shot, as Romanoff approaches the Quinjet and Steve and Coulson exit, we can see one of the wings is completely open. (00:30:35)
Factual error: During the scene on the Helicarrier where Bruce Banner "Hulks out" and jumps at the F-35B hovering just outside, we see the F-35B fire its guns, one inside each of its intakes. The F-35B has only one gun, externally mounted to underside of the fuselage. It would be impossible to mount a gun inside an aircraft's intakes.