What Batman does seems slightly unfeasible.
Think about it. He goes out night after night and fights criminals in Gotham City. But how does he do this? He waits until it's night. Night time will generally be from 7:00 pm to maybe... what, 5:00 am? That's not bad, that's a solid 10 hours of crimefighting. But what happens when the sun comes up? No more Batman. And that's exactly when the criminals and supervillains are going to strike, right? Cause after a while, even the cowardly and superstitious lot are bound to notice that Batman seems to arrive at 7:00 pm every night, like clockwork. They'll just sleep during the night and do their dastardly schemes during the day. Kinda like how normal people operate. Batman isn't able to do anything, he's gotta wait till night. Unless he got some sort of WayneTech device to block out the Sun. That'd be silly, though.
But you might be saying... well, he'll just go out as Bruce Wayne during the day and stop them with his Lamborghini Murcielago. Like in that Chris Nolan film, The Dark Knight. Which sounds good, except that he actually risks blowing his cover. He's not wearing his mask as Bruce Wayne. And Bruce Wayne doesn't have the protection of the Batsuit, or any handy gadgets. That's quite risky. So what he did in TDK seems like a pretty rare occurrence. Generally, he's not gonna risk it.
And of course, he'd probably be sleeping during the day. Like a vampire, which is appropriate. After fighting crime for 10 hours and grappling from building to building, beating thugs, saving hostages... Bruce has got to be beat and in need of some rest. I don't believe any comics have ever had him copying Kramer and trying that DaVinci sleep method where you only sleep for 20 minutes every few hours or something. The man's reserves are down, he'll have to go to sleep during the day. You know what happens when he doesn't get sleep? He gets his fucking back broken, that's what. It's a bad scene.
Now, on to Batman actually fighting crime. His batsuit protects him from bullets. And he'll generally hide in the darkness. But what about his no killing rule? Is that really an actual rule that a guy fighting crime night after night can keep? You'd think that eventually he'd do something like punch a guy, have the guy go unconscious, fall down, hit his head on a toilet bowl or something, and die from inadequate medical attention later on. Or maybe he punches some big dude in the chest, which causes a freak heart attack and death? Ya know, stuff that's a little unlikely, but becomes more and more likely as his crimefighter career continues. Batman doesn't have detailed medical dossiers on every two bit crook and thug in Gotham, right? That seems like a stretch.
In law, we have something called the eggshell skull rule. Basically, if you punch someone in the head and they turn out to have a rare condition which makes their skull as weak and brittle as an eggshell, you'll be punished for the actual outcome, not your intent to merely inflict a punch that would have slightly injured a man with a normal skull. So you're basically screwed if you just happen to punch someone with an eggshell skull. Now, this could happen to Batman. He might not know if a new criminal mastermind has an eggshell skull. So he goes for the one punch knockout and... ends up killing the guy. Gordon and the GCPD suddenly have a warrant out for his ass. He's done for. Or, the criminal supervillains like Joker or Two Face could just hire someone with an eggshell skull to be their thug for a heist. Batman shows up and falls right into their trap. It's terrible, breaking your one rule to never kill because you ran into a thug with an eggshell skull. That would just feel terrible.
Batman often gets wounded in combat. You know, something sharp shreds his costume sometimes. Catwoman's scratched him good in a few encounters. So he gets cut a bit and maybe blood spills out from the wound. Batman doesn't stop to clean up the pavement, he just keeps going with the battle and drives away when it's all over. So you've got Batman's blood on Gotham pavement, or inside a building somewhere. Couldn't someone take that blood and try to find Batman's real identity with it? Just gotta try and match it up with any DNA in a database. Bruce Wayne probably had blood taken from him as a kid for... medical reasons, right? Does a hospital keep really good records of people's blood and DNA? I'm not sure, but even if they don't, the existence of Batman's blood is worrisome evidence. Could you use the DNA in the blood to trace it to the Wayne genealogy? It doesn't seem too far fetched.
It's tough being Batman. I don't know how he does it.