Continuity mistake: In the final battle, Wasp and Ant-Man are in the van trying to get the quantum tunnel operational. We cut back to the fight and we can see Ant-Man there too, fighting in his giant form. (02:22:20 - 02:23:00)
Factual error: Twice in the film it is made clear that the Pym particle works by reducing the space between atoms in order to shrink an object, and by increasing it to enlarge them. This means that the object will weigh the same, whether shrunk or enlarged - it cannot be otherwise. A 90kg man the size of an ant would punch a hole through any surface upon which he stood (and couldn't ride ants), Doctor Pym has been walking about with a 60 tonne tank in his pocket, Darren Cross lifts a full grown sheep between finger and thumb, and the supersized Thomas The Tank Engine would be far too light to crush the police car (in fact it would float harmlessly away as it would probably weigh less than the air it displaced).
Factual error: When the bus is shown entering Washington, DC for the competition, the shot shows the bus traveling over the Arlington Memorial Bridge with the Lincoln Memorial in the background. That bridge is on the southwest side of the city. Since NYC is to the northeast of DC, this means that to get to that bridge and enter DC that way, the bus had to drive all the way around the city and then come back in from the opposite direction. Even if the bus driver made a mistake and missed the most direct route into the city from the north, there are dozens of other ways to get to the heart of the city without adding a good 45 minutes to an hour to the trip.
Factual error: In the first scene where Dr Strange is preparing for surgery he uses improper surgical gowning technique breaking aseptic protocols. Strange puts on a mask after washing his hands, contaminating his clean hands by bringing them in proximity to the non-sterile environment of his face. Surgical masks must be worn before the full washing of hands. Another error is that he inserted his hands all the way through his gown to don gloves. Hands must never leave the sleeves and gloves must be put on with the sleeves still covering.
Factual error: In the final fight scene with Malekith, Thor falls through a portal that brings him to Charing Cross station, where the lady on the train tells him he has to ride 3 stops to get to Greenwich. Charing Cross is not on the Jubilee Line and so not directly connected to Greenwich - even then it's a lot more than 3 stops. (01:33:45)
Character mistake: When Harley asks Tony what the light is coming from his chest, Tony responds "an electromagnet." Harley replies "What does it power?" An electromagnet is not a source of power. The arc reactor is the power source which powers both the electromagnet (to keep Tony safe from the shrapnel near his heart) and the Iron Man suit. (00:43:25)
Continuity mistake: On the spaceship, Peter is talking to Tony, and has his hair swept back with gel or similar. When he says "You can't be a friendly neighbourhood Spider-Man if there's no neighbourhood", we cut to Tony then back, and Peter now has a fringe with no gel. In later shots it's back how it was before.
Continuity mistake: When Peter and MJ hug on Tower Bridge he gets some blood from his face onto the left shoulder of her jacket. From other angles there's no blood.
Continuity mistake: During the street chase in Brazil, the time of day changes from night, to perhaps late afternoon/evening, to night again.
Factual error: When the action moves to England after the failed award ceremony, the British Union Flag hanging from the wall is upside down. The broad white band should be at the top left (nearest the top of the flag pole).