Couldn't have done it if Batman didn't bring in Lau from Hong Kong.
The legalities of Batman are never really made clear. They specifically show that all of Gotham, as well as the GPD know that Batman, Gordon and Dent are working with each other. Batman shows up at crime scenes for god's sake! Isn't Batman a vigilante, isn't that illegal? TDK walks a fine line of going the 60's route in giving Batman a badge.
Lau being brought in by a criminal wouldn't fly (lol), neither would the RICO case.
So Dent is basically a better role model than Batman because he doesn't wear a mask. Yeah, I get it, and that's the intent, clearly, but damn if it isn't a contrived one. That's one of my biggest problems with this series. The fact that Batman wants to "inspire" something other than fear. Batman's above the law, countless of stories depict this. In fact in Batman's mind, his views and ideals are his law. He shouldn't even be working with the police. By the end it's actually a "GOOD" thing that he's being hunted because he's back to square one. It was cool in Begins seeing young, college student Wayne question "justice" and saying that the system and ____ doesn't work. Then that's quickly done away with when he's babbling on about inspiring hope in others and wanting a new DA on the block to take his place.
Batman and Dent should not like each other.
It's not just TDK walking a fine line. This is actually not a radical departure from other interpretations of Batman in the comics and the animated series. Batman is a vigilante, and yes that is illegal, but Gordon always maintains plausible deniability. When Dent asks him a direct question about Batman-
Gordon: "Official policy is to arrest the vigilante known as Batman on sight."
Plausible deniability.
Even though Gordon, Dent, and Batman conspire to extradite Lau from HK, the public doesn't know this, and when Lau--a wanted man-- "randomly" gets delivered to Police HQ, there's no evidence that he was brought in illegally by a vigilante, and it's not in the interest of the cops or D.A. to dig too hard to find out how he got there. When a reporter asks Dent directly if Batman had anything to do with bringing Lau back-
Dent: "I don't know about Mr. Lau's travel arrangements, but I'm sure glad he's here."
Plausible deniability.
I think it's reasonable for both Dent and the cops to have a favorable opinion of Batman, and want to work with him (at least early in the film, before he becomes a "villain" in their eyes). Yes, he's a vigilante, but he's clearly no amateur like his acolytes, and he gets results. He's out there assisting them without screwing up and making a bigger mess for them to deal with like an amateur crimefighter would. Secondly, they like him
because he is an illegal vigilante. This comes up often in the comics. Batman's hands aren't tied by the law and due process. He will do almost anything necessary in the name of justice. Ever see a cop dangle someone off a ledge to get info from them? Dent and the cops have to be frustrated, especially in a town like Gotham where so many criminals can walk or game the system to get off. It's nice to know they've got someone on their team that also isn't "playing fair". Gordon and Dent are sworn to
publicly uphold the law, but they understand that in a town like Gotham, sometimes you've got to
privately bend the rules in the name of justice to get things done. "Like" is probably too chummy sounding of a word, but of course Batman and Dent respect each other, and see the advantage of having the other around as an ally. In Year One, Frank Miller even has Batman form an alliance with Dent
before he forms one with Gordon.
Still, Nolan shows that some cops are peeved by Batman's involvement at crime scenes. Ramirez speaks up about him a few times (which is ironic, since she herself was compromised).
Batman has always skirted the line between what is legal and illegal, it is not a dilemma new to this series. "Officially" the police can't sanction or even condone his involvement, but he still operates with some rules in the majority of the comics---he doesn't view himself as the final judgement on the law. He's still got his one rule, and Gordon has warned him that he would lead the charge to bring him in if he ever crossed that line.
There's several clues that Gordon knows exactly who Batman is (in the comics, and in this specific film series), but he's not going to give up his plausible deniability to arrest someone that does so much good.