General Ross has received word that fugitive Bruce Banner will be at Culver University. This is his chance to capture him. You'd Expect: Ross to order his men to try to capture Bruce stealthily, so that he'll has less time to become agitated and thus transform. Once captured, Bruce will be unwilling to transform because he knows he's in an area full of civilians. No one will know they were there. Instead: He orders all his men to charge into the university in broad daylight, alerting Bruce and Betty, causing panic amongst the students and teachers, and agitating Bruce enough that he transforms soon after they get to him. Then that leads to a whole lot of property damage...
Thor's Awesome Moment of Crowning is interrupted by an attempt by Frost Giants to steal a MacGuffin from Asgard. Thor is furious at the Frost Giants for ruining his big day and making Asgard look weak, and wants to take action, despite his father Odin, who happens to be the King of Asgard, showing open disapproval of such ideas. You'd Expect: Thor to sit tight in Asgard and not do anything reckless. Instead: He lets himself be manipulated by his brother Loki into storming into Jotunheim with some of his friends, which causes a fight to break out between Thor and Co and the Frost Giants. These actions cause the Frost Giants to issue a declaration of war on Asgard, and get Thor stripped ofhis powers and banished to Earth, in order to undergo Character Development. Also: Thor seems to have no idea of the fact that Odin isn't a fan of war; when Odin shows up in Jotunheim, Thor immediately assumes he's there to help him destroy the Frost Giants. As Odin rightly admits later on, he was a fool to think Thor was ready to succeed him.
Steve Rogers is recovering from about 70 years on ice. The powers that be elect to lessen the shock by placing him in a mock-up of a recovery room and not letting on how much time he had been out until they could perhaps break things to him gently. You Would Think: At bare minimum, they would have the "radio" playing period music or if they insisted on a "live sports broadcast" they would take care to pick one that took place after Rogers vanished. Instead: They have a Brooklyn Dodgers home game from 1941 playing. Even if they did not know Steve had attended it is a matter of public record that he was still living in Brooklyn at the time.
Loki arrives at Earth and brainwashes Clint Barton (aka Hawkeye), Eric Selvig, and another agent of SHIELD. Fury is the only person in the room that is not brainwashed, and Loki wants the Cosmic Cube. You'd Think: Loki would find value in Nick Fury and also brainwash him as well, since he is the director of SHIELD. He can then have Fury as his puppet and manipulate SHIELD so that he can get away with his plans. And then the Avengers would never have been assembled. If he eventually thinks Fury and SHIELD is no longer valuable, he could then pull off a "You Have Outlived Your Usefulness" on both SHIELD and Fury. Instead: He doesn't value Fury at all, only viewing him as an ant. He only takes the briefcase, having Hawkeye kill Fury. He fails to do so, and Fury survives to lead the fight against him.
After the explosion at the TCL Chinese Theater, Tony Stark personally declares war on the Mandarin and dares him attack Tony, on international television, and then goes home. You'd Expect: Tony to take precautions and ready his house for defense at all times, and put on a fully operational and perfected Iron Man suit (i.e The Mark VII), in case there's the off chance the enemy suddenly attacks. Either that, or at least get Pepper Potts out of harm's way. Instead: Tony sits around and waits for the attack, and the only precaution he takes is going into an ineffective lockdown, and has no fully-functional suit ready to go.
Tony's home has just been destroyed by the Mandarin's (Killian's) forces, and Tony is knocked unconscious during the attack, but survives thanks to J.A.R.V.I.S. taking control of his suit and flying him away from the danger zone. You'd Expect: J.A.R.V.I.S. to fly just far enough to get out of danger, and wait for Tony to regain consciousness, so that he can decide on a course of action. Instead: J.A.R.V.I.S. decides to fly Tony all the way to Tennessee, simply due to the fact that Tony was planning to go there at some point to investigate the Mandarin. Never mind that Tony might have other plans, like protecting Pepper, or switching to a better suit. Worse, due to this suit being a Flawed Prototype, the flight uses up all of its power, and Tony is rendered pretty much helpless untill he can recharge the suit/make improvised weapons.
Rhodey gets captured by Aldrich Killian's ( The actual Mandarin) mooks, and is forced out of the Iron Patriot Suit by Killian's Extremis Heat. They then knock him out unconscious. You'd Think: Killian or one of his goons would either: a.) Tie him up so that he can't escape the mansion. or... b.) Since he was a commando, and a potential enemy, kill him, so that he won't wake up. Instead: They just leave him there, and he eventually regains consciousness and links up with Tony, who also has escaped captivity as well.
After the above moment, Eric Savin, Killian's main henchman, uses the Iron Patriot suit to pose as Rhodes and infiltrate Air Force One. He arrives at Air Force One as President Ellis gets on board. You'd Expect: Before taking off, the security guards to check who is in the Iron Patriot suit (especially since Rhodes had been AWOL for about half a day, and the exact suit had been commandeered in the previous movie), and find out that it's Savin and incapacitate him, thus averting disaster. Instead: They don't even bother to check and just assume Rhodes was still in the suit. The Result: Savin manages to attack and destroy Air Force One, and have the President of the USA kidnapped in the Iron Patriot suit.
The final battle. On Tony's side we have Tony, James Rhodes, and a load of Power Armors much like the ones Tony wears, remotely controlled by J.A.R.V.I.S., while on the Big Bad's side we have a load of superhumans who can regenerate from damage, and make parts of their bodies extremely hot. Tony has encountered them before, so he knows what they're capable of, and he's here to rescue two hostages. You'd Expect: J.A.R.V.I.S. to keep the suits out of range of the minions, and bombard them with repulsor rays, in order to keep them distracted while Tony and Rhodes rescue the hostages. Instead: The suits controlled by J.A.R.V.I.S. are often seen getting into punch-ups with the minions, and a number of them are torn apart as a result.
When Thor and Loki go to Svartalfheim so that Malekith and the Dark Elves don't go to Asgard to launch another attack, that would definitely cause them to win, Thor and Loki get into a brawl with Malekith's main henchman, Algrim (who at this point, in the monstrous Kurse). Kurse stabs Loki before he is killed by an activated black hole grenade on his belt. Loki however is not really dead, and fakes it in a Died in Your Arms Tonight moment with Thor. You'd Expect: Thor to check for a pulse at the very least to check if Loki is Faking the Dead, after all, he tricked the Dark Elves into believing he cut Thor's arm off earlier, and he is The God of Mischief, so he's probably faking his death. Instead: Thor falls for the Faking the Dead, doesn't even check for a pulse, and thinks Loki died, and leave him on Svartalfheim while he and Jane Foster find a way back to Earth. The Result: Loki escapes Svartalfheim disguised as an Asgardian soldier, and usurps Odin (whose ultimate fate is unknown) while Thor is busy fighting Malekith on Earth.