I think the Riddler could contribute very well to adding an element of "mystery/suspense" to the series. Here's a concept I've been mulling around:
We see Edward Nashton. We do not see The Riddler. We can use The Departed as somewhat of an inspiration here, in that Nashton is brought in to investigate a series of Zodiac-style murders (the difference between the two, however, is that the Riddler leaves riddles that, when solved, tell the police both where the next murder will be and who the next victim is, but doesn't delve into the particulars.) but over the course of the film it becomes apparent that Nashton and Riddler are one and the same.
At the same time, we have Batman investigating the Riddler killings covertly, constantly pursued by the GPD. To make matters worse, a common catburglar arrives on the scene, making it more difficult for Bats to operate. On the other end, Bruce's high-school sweetheart Selina Kyle returns to Gotham, and she and Bruce begin seeing each other. However, Bruce struggles to move on after Rachel's death, making his and Selina's relationship very awkward. Also, it's unclear what Selina's/Catwoman's motives truly are, as she steals from wealthy corporate CEOs with dirty laundry, making her something of an antihero.
I like this idea, but I don't like the idea of the Riddler being a common serial killer. the Riddler, even at his worst is'nt someone who enjoys killing in the comics. He is about proving himself, and is willing to let people die for it, but he does not enjoy it in the way The Joker or Black Mask do.
Because of this, instead I would make Nashton someone called in by the police to investigate murders like you said, but he is actually secretly working with the murderer, to keep his name clear, who is Black Mask/Roman Sionis and is doing the killings to advance Janus Corporation. Nashton invents the Riddler persona to throw off Batman from the real trail and lure him out. Again its not heavily important we see the Riddler in costume except through maybe a fake police sketch.
Catwoman can be an in between person, and we don't know where her loyalties lay until the end (perhaps she doesn't even know herself). She could start out as a suspect as the possible killer (along with Batman) with confusion laying in the fact that they all wear all black costumes (Black Mask, Batman and Catwoman). Somewhere in the middle of the film, she is recruited by Black Mask who says that if she helps him find out who Batman is, he will let her off for all the money she has stolen from him. She agrees to this, finds out Batman is Bruce, tells Black Mask and the Riddler who set up an intricate trap for Batman/Bruce Wayne to humiliate him and eventually capture and torture him, but in the end decides she is in love with Bruce/Batman and saves him. After the main climax, (which where Black Mask is killed and The Riddler gets captured) Batman talks to Catwoman and says, because she is a criminal, he cannot be with her. He does lets her go instead of capturing her though. She starts to run, but in the end turns herself over to the police.
Characters
Batman/Bruce Wayne: Batman is still on the run from the cops. Despite the fact he is still fighting crime, the cops are using him as a scapegoat and trying to pend him as the Black Mask killer. Batman himself is actually quite close to solving the mystery of the killer, having almost captured him once only to be interrupted by the appearance of a mysterious cat burgler. Bruce Wayne is not doing so great either. Still distraught over the death of Rachel, he has almost completely given up on social interaction save for with Alfred while Wayne Enterprises has recently lost a large government contract to Janus Corporation who managed to somehow acquire a piece technology last minute that Wayne Enterprises had spent years developing.
The Riddler: The presence of at least two black costumed figures running amok in the city has caused the police great distress and left their own detectives baffled. Finally fed up with the lack of progress in catching Batman or proving him to be the Black Mask killer, the Mayor orders Gordon to call in "an expert". Ed Nashton, a former codebreak turned private investigator is hired to track down the Batman and prove he is the Black Masked killer. What the police don't know however is that Roman Sionis, the real Black Mask, has already gotten to him and made a deal. He will help him solve the riddle, "Who is the Batman?", if Nashton promises to help him keep his name clean and turn the Batman over to him once he is captured. To lure the Batman out, Nashton invents the persona "The Riddler", leaving riddles that lead Batman to various points where he can be captured and framed as the Black Mask killer.
The Black Mask: Roman Sionis is the newly appointed CEO of Janus Corporation. While at first he seemed to be running the company into the ground, the minute he realized he could use criminal activities to bolster his company things turned around. The first victim of the Black Mask is a former intern at Wayne Enterprises who Black Mask captured and tortured into receiving information on technology that could advance his company, the next string of victims are all various other corporate targets who's death can advance Sionis but in a none obvious way. After almost being captured by Batman, Sionis turns to Nashton, someone who he previously used to spy on his victims before their murder, to infiltrate the police department and lead them astray. Nashton agrees on the condition that he use his corporate power to help him capture Batman. Sionis also has a personal rivalry with Bruce Wayne, with slight hints that they have a past together. This causes Sionis to seek to not only demask Batman once he finds out who he is, but humiliate, torture and kill him.
The Catwoman: While at first simply a cat burgler, after her encounter with Batman and Black Mask while attempting to steal from a powerful businessman that Black Mask intends to murder, she realizes that in order to go toe to toe with these freaks, she needs her own form of standing out and her own scare tactics. Having an affinity for cats, she takes on the costume. Meanwhile as Selina Kyle, she has become the Heroine of the East End and has started a large charity with stolen funds that seeks to revitalize the area. She meets Bruce Wayne at a charity function he attends by Alfred's demand, and becomes enticed with him and his depression. Bruce, suspicious of her sudden rise to fortune accepts a date from her, and invites her to Wayne Manor. On the date, he manages to find they actually do have a lot in common and begins to like her, however she does scope the mansion, planning to come back and steal (showing for her, the life is almost like an addiction, she steals even from those she likes), and discovers he is Batman. Having a deal with Black Mask, she turns this information over to him in exchange for being let off for stealing from him.
The main theme of the movie is of course, riddles but also the blurring line between good and evil, and abuse of power.
The movie would be set up like a giant riddle, with at any one time, you don't know quite where anyone's loyalties lay. In fact, you could even set the movie up like a riddle, starting out with a sequence from sometimes toward the end of the movie showing newspaper headlines or something saying "Batman charged with over 40 murders", or "Batman: The most dangerous criminal alive". Then Alfred's voice asking "How could this have happened?" Before you cut to the story, showing the answer.
