In one of the first scenes of the movie, a gang wearing clown masks robs a mob bank. They constantly shoot and kill each other to get a larger share of the money they steal. The manager fights them, but is overpowered and captured. Bozo (really The Joker in disguise, kills Grumpy by running him over with a school bus that is the getaway car. The manager sees all this. You'd Expect: That the manager just keeps quiet, since Bozo was walking away and obviously not going to kill him. Instead: He shouts at Bozo, asking him what he believes in, causing Joker to reveal himself and put a gas grenade in the managers mouth. Granted, this was needed to show the Joker to the audience, but COME ON.
Dent spends the first half of the film half-criticizing/half-warning Gordon that there are dirty cops in his unit that can't be trusted. You'd Expect: That Gordon would listen to Dent (if he isn't already aware of the fact that he does have dirty cops in his unit) and perhaps even coordinate with him to root out those who are least trustworthy and reassign them to positions where they can't interfere. It is Gotham after all, and Gordon's been in the game long enough to know how corrupt the force is. Instead: Gordon blows off and ignores all of Dent's warnings for whatever reason, whether because he doesn't trust Dent or thinks Dent has no right to criticize him since he didn't come up in the GCPD etc., stubbornly insisting that he has to do the best he can with what he has. This ultimately comes back to bite everyone in the ass when Wurtz and Ramirez, who work under Gordon's team, are ultimately revealed to have been working for the mob and by extension the Joker.
After the Joker is arrested, he's put in a secure room for interrogation. While inside there he's handcuffed and the door locked, although both are removed as the interrogation goes... physical. Eventually, though, the police and Batman get the information they need and rush out. You'd Expect: The remaining police would have shackled the Joker and lock the cell's door from the outside as well. The room has huge windows, so they can see if he starts trying to break out. Instead: They leave him un-handcuffed and put one policeman inside the cell to guard the door. After provoking Stephens into fighting him, the Joker overpowers the cop, holds him hostage, then initiates his breakout plan.
The Joker is in the cargo hold of a ship, burning down money. The police know he's there and are going to deploy a squad to capture him. Then they hear that the Joker's going to blow up a hospital in an hour. You'd Expect: That they'd split the group in two, sending some men to evacuate hospitals or disarm the bombs in them, while others storm the ship, incapacitate the Joker and thus end the madness. Instead: They abort the operation and send every cop to evacuate the hospitals and while letting the Joker escape, which almost causes the complete collapse of Gotham into anarchy.
Batman was forced to kill Harvey Dent after he went mad from grief and killed five people in a revenge spree. But the public reveres him as a hero, so Gordon and Batman fear that telling them the truth, that their hero snapped and became a murderer, will demoralize them. They decide to blame the murders and Dent's death on someone else. You'd Expect: They'd claim the murders were done by the Joker, who kills dozens of people every day on a whim. A few more deaths can be easily pinned on him, and who would believe him if he claims he didn't do it? Instead: Batman himself takes blame of the deaths, causing the public and the police to turn against him. In danger of being arrested, Batman goes into hiding and his career ends for eight years.
Carrying over from the end of The Dark Knight, Alfred has kept Bruce completely ignorant of the fact that Rachel Dawes chose Harvey Dent over Bruce himself, since Rachel ultimately felt that she could never be with Bruce due to his obsession with being Batman. You'd Expect: That at some point Alfred, who knows that Bruce doesn't have the best mental health, would have told Bruce the truth and help him come to accept the fact that it wasn't meant to be - in more ways than one - and then help Bruce move on with his life and live like a normal person, which is what everyone, even those who don't know the truth, really want for him, and is most certainly what Rachel and his parents would have wanted for him. Instead: Alfred continues to keep the truth from Bruce, hoping that one day Bruce will at least learn to make peace with the fact that there are some things that can't be changed or controlled, such as the losing a loved one, which is "all part of living" after all, as Alfred points out early in the film. As a result Bruce spends the next eight years just sitting around his home in a depressed funk, believing Rachel was his one true love and soul mate and refuses to move on since he believes he can never find another love that was as, ahem, pure and true as what he had with Rachel, and secretly hoping that things will "turn bad again" so that he can go out and channel his rage into fighting crime as Batman again. When Alfred finally does tell Bruce the truth he doesn't take it very well.
Foley and Blake tell Gordon, who is in the hospital from being shot by Bane's henchmen earlier, about the possibility that Bane is hiding in the tunnels. Gordon wants to smoke them out. You'd Expect: Gordon, having been a GCPD cop during the times of both Ra's al-Ghul's and the Joker's attacks, to consider the possibilities of the sewers as a trap and maybe send only a small but elite team (maybe just one SWAT team and a couple of less important officers) to investigate the tunnels, so that if a trap did go off, they still have a decent enough force to deal with any future riot or hostage situations that might occur. Some would notice, but not a huge loss. Or alternately, just not send any cops into the sewers at all and keep them all on the streets, forcing Bane to have to change his plans. Instead: They send the entire police force into the sewers, which leads Gotham to go downhill, because Blake doesn't find out the explosive trap until it's pretty much too late, after all the cops have basically gone into the tunnels, and Bane sets off the explosives, and traps the cops underground, leaving Bane and his men free to invoke their Reign of Terror on the town.
While the police was investigating the tunnels, Bane arrives at Wayne Enterprises and makes Miranda Tate and Lucius Fox scan their hands, so that he can steal the reactor. You'd Expect: Lucius to pull off an I Surrender, Suckers, and secretly activate the emergency flood chambers, which would then throw a monkey wrench into Bane's plan to steal the reactor. Instead: He plays it all real and scans his hand, allowing Bane to take the reactor and hold Gotham City hostage with it. It could be argued that since Miranda Tate is in fact Bane's accomplice Talia al Ghul, that Bane would have known what Fox was doing, but still.
Also from the same movie: After Batman beats down Bane, he demands to know who "the triggerman" is. It turns out to be Miranda Tate, who is in fact, Talia Al Ghul, the daughter of Ras Al Ghul. She then stabs Batman in the chest. And she has the detonation remote. You'd Think: Miranda/Talia would simply press the remote and detonate the nuclear reactor and nuke the area instantly. Instead: She wastes time twisting the metaphorical knife (to match the literal one) delivering a long expositional monologue to Batman, giving time for Commissioner Gordon to plant the device to block the reactor's remote signal so that she would not be able to detonate it right away. And she knew that's what they were trying to do, and deliberately directed them to the wrong truck earlier. Nice Job Fixing It, Villain!!
Near the end of the movie, after stopping Miranda Tate (Talia Al Ghul), the heroes have to somehow stop the reactor from destroying Gotham. Unfortunately, Talia has flooded the basement where the reactor is supposed to be kept. You'd Expect: Talia to keep her mouth shut about flooding the fusion reactor basement to the heroes, so that they would have continue to waste time dragging the reactor to the location to attempt to reconnect it, which would be in vain, and thus, the reactor would blow up! And then Talia would have succeeded. Instead: Talia, drawing her last breath, says about the reactor basement flooding, and gloating to the heroes to prepare themselves for their dooms. Batman then manages to fly the reactor miles away from Gotham as it explodes and foil Talia's scheme. Very Nice Job Fixing It, Villain!!