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.
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.
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.
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 wouldn't count 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.
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.