Here's the game I would love to see for The Dark Knight:
1. Free-roam. Use a variation of the Assassin's Creed engine with the added ability to glide or use the grappling hook as means of travel. Also have access to the Tumbler, and be able to call the Tumbler to your location at any moment. Tumbler would act as your inventory hub, allowing you to switch out gear and fast-travel if necessary.
2. Interrogation system: Grab thugs, drag them to the top of a building and use the analog sticks to dangle them over the edge. Do it just right and you get the info you need. Do it wrong, and they have a psychotic break, viewing you as "the demon batman" from Batman Begins. They become useless and the knowledge is lost.
3. Detective Work: Find clues, work with Gordon to nail suspects, listen-in on mob meetings from across the street, etc.
4. The game starts before the movie, bridging the gap between Batman Begins and TDK. After the destruction of the Narrows, most of the Arkham escapees were rounded up by Gordon and his newly-minted Major Crimes Unit. That being said, a couple escaped (Ventriloquist, Bane, Poison Ivy, and of course, Scarecrow). You play through a storyline for each escapee, tracking them down and taking on the threats they present. Ultimately the storylines converge into an overall plot where you hunt down the Scarecrow, finally resulting in you walking right into the opening scene of the movie. From that point on, the game would follow the story of the movie as closely as possible while remaining "fun" (i.e. some liberties can be taken where necessary).
5. Keep the game alive: Don't know why other hero games don't do this. After you complete the game, in addition to random crimes, occassionally there would be a "break-out" where one of the major villains (the aforementionable escapees and the Joker) get out of Arkham and you have to track them down and fight them. These would be simple 1-2 part side-mission that would be randomized.