So this is removing the suspension of disbelief. DON'T READ THIS IF YOU JUST LIKE BATMAN AND DON'T WANT TO RISK RUINING HIM.
So the path is like this.
1) Batman has made Gordon break the law.
Batman is a vigilante in most forms I see him, and he is breaking the law. Working with a commissioner the way he does without being a law enforcer he can get Gordon in trouble. If he is a law enforcer he has state he is when he is making the arrests.
2) Money trail
The only way batman can have all his gadgets is through Bruce's money. He would have to either buy it all which would leave a trail that can probably be traced. Or he steals it from Wayne Industries which would have records of them, and still would have the tech there. Anyone who takes this trail probably would locate who he was.
3) Electric bill
So Batcave alone must be high as hell on the electrical pull. Now that much power being drained probably raises questions. However Batman has his own private generator. How much power does that cave need? I am going to assume a pretty large draw for everything in there. No one notices this secret power supply? It can't be a tiny generator people keep for flooding. This though I can believe not being noticed.
4) His villains.
Yes most are crazy people that do what they do many through Batman or other masked figures. Though makes you wonder what if the villains are like actors paid to do their bits, they play crazy commit crimes, draw attention to certain things. Batman saves the day, he gets seen as a hero, politicians or companies get to fix the attention at hand, the villain goes to Arkham which they could basically be on vacation until it's their time again.
5) The sidekicks.
No one ever questions why Robin suddenly exists with Batman about the same time Bruce Wayne gets an adoptive son (one biological). It just that simple, no one questions it I think a lot of people know who Batman is they just let him think it's a mystery.
6) Corruption
Friend of mine said he could just cover up his expenses. Well he could but I don't see Bruce Wayne doing that, that is expensive and against what Bruce does usually digging politicians and businessmen covering up their activities. Granted Mr. Wayne could be a hypocrite but then he'd be a hypocrite.
Is this debunked by it being a super hero? I guess it is, but what if Batman is just this political puppet actor, who lives this fantasy fighting other actors. Batman feels good about himself, Villains get paid, companies and politicians can advance properly or hurt competition, and the public gets an icon.
What do you think of Batman just being a hoax? Could you believe it or do you think Batman could be the real deal?
