Batman tells Carrie Kelley, the new Robin, at least twice, that if she ever disobeys his orders she will be fired. Carrie in fact does so, on at least three different occasions, yet continues in Batman's employ. Batman not following up on his threats, especially when it comes to flouting his authority in life-threatening situations might seem wildly out of character, but not so much if you consider the circumstances. Robin's unauthorized reprogramming of the "Batcopter" was the only thing that enabled Batman to escape the police at the beginning of chapter 4, and this was due not only to Carrie's ingenuity and technological acumen, but her ability to think creatively and outside the box. Notice that he actually smiles. This older Batman may feel out of touch not only with modern technology on the whole, but has also (after the losses of at least two other Robins and the subsequent years of loneliness) learned to appreciate the viewpoints and perspectives of others, especially those he is partnered with. Kudos to Bruce Wayne/Batman for actually growing (somewhat) as a person over the decades.
Two-Face, unlike the Joker, did not return due to the reemergence of Batman: Harvey Dent relapsed and became fully consumed by his evil side long before Bruce Wayne put the cape and cowl back on, totally refuting quack psychiatrist Bartholomew Wolper's theory that Batman is ultimately responsible for the creation and crimes of his rogues' gallery. Yet on a very basic level, Batman still probably blames himself for Harvey's plight, as it was his money (as Bruce Wayne) that funded the ham-handed efforts of Wolper and plastic surgeon Dr. Willing to "cure" Two-Face, which only succeeded in bringing Two-Face to the forefront, probably permanently.
At first, Bruce/Batman missing his shots just after the death of The Joker seems silly...until you realise, this is probably the first time he's used a pistol.
The aftermath of the electromagnetic pulse that knocks out Gotham's power is implied to have taken out electricity across most of the United States, and due to proximity at least some of South America as well. And a news report specifically points out that only Gotham has maintained law and order thanks to Batman. Not only did countless people die due to the failures of vehicles (including an on-screen plane crash) and devices, the whole nation descended into anarchy and chaos with the military pulling martial law. And this is a world where Superman and the U.S. effectively dismantled the whole of the Justice League, meaning superheroes are essentially outlawed at worst and distrustful of the government at best. All it took was one nuke that Superman managed to stop from blowing up an island, to cause permanent damage and nearly destroy the whole nation indirectly.