Well, predictably, the moment TDKR came out, speculation already began on the nature of the inevitable reboot. And while we know absolutely NOTHING about the next incarnation of the Dark Knight on screen (well, apart from the fact that he'll be less 'realistic' than Nolan's version and might tie-in with a Justice League movie), these are a few things I believe ANY director/screenwriter needs to keep in mind while planning the Batman reboot-
1. NO ORIGIN. That's the MOST important thing of all to keep in mind. Everyone knows the story already, and Nolan did it probably better than anyone else ever will in Batman Begins. Time to move on. Nolan has done a great origin story and a great 'concluding chapter' to the Dark Knight legend...time to focus on the MIDDLE of Batman's career (which is what 90% of Batman stories have focused on anyway - so there's PLENTY of source material and new avenues to explore). I want to see a Batman who's several years into his career and well-established in Gotham City as its protector and resident hero. Of course, a flashback to the Wayne murders WOULD be a welcome move and a poignant moment in ANY Batman story, especially if it relates to a moment in the central narrative...but no more 'Year One' era!
2. Avoid re-hashing the Nolanverse villains. Nolan did a perfect Ras al Ghul, Scarecrow, Two Face, Joker, Catwoman and Bane. While these are are legendary villains in the Batman lore-indeed, some of them being his greatest villains EVER, Nolan's take on them is still fresh in the public memory (especially Heath Ledger's Joker) and there are MANY great villains who've either not been on screen in a while, or have NEVER been on screen. In the former category, we have characters like Riddler, Penguin, Mr. Freeze etc. And in the latter, we have the likes of Hugo Strange, Clayface, Harley Quinn, Mad Hatter, Deadshot, Black Mask, Killer Croc and so many others. There's a whole galaxy of villains for the new series to explore, before they consider reinventing the Joker again (which is also pretty much inevitable at some point).
3. Related to the above point - it'd be great if we got to see more characters and concepts from the Batman mythos which haven't appeared in previous films. For instance, I'd love to see prominent characters from the GCPD like Harvey Bullock or Rene Motoya (granted, Anna Ramirez from TDK was supposedly based on her, but still). Or Leslie Thompkins (and related to her, the whole idea that Batman visits Crime Alley once a year to pay tribute to his parents...which made for one of the best episodes of the TAS). Also, how about we get to see a Batcave with a trophy room, including a robot T-Rex and a giant penny! Or Batman's 'Matches Malone' disguise. The possibilities for world-building are endless!
4. Stylistically speaking, the reboot should go in a totally different direction from Nolan or Burton (and definitely STAY AWAY from Schumacher!) And I think a good way to go about it is to embrace comic book aesthetics for once rather than avoiding them. 'The Avengers' has proved that you can use the comics books as a direct stylistic influence on films and still manage to get away without looking unduly silly and campy (in fact, you get away looking AWESOME!) So, for instance, I'd love to see Batman with a more 'comic-book' based costume, with a grey bodysuit instead of the all-black look ALL the movies have had so far (the current 'New 52' suit can serve as an ideal template IMO). I'd love to see the villains in costumes based off their comic book appearances...not uber-realistic but certainly not campy and over-the-top. The Batman universe on film should look and FEEL like a world where a woman can walk around in a green dress and wrapped in vines, along with an obese man in a tuxedo carrying trick umbrellas, and a monstrous-looking man with scaly skin...and still look deathly serious. The kind of tone they should be aiming for is something akin to the TAS.
5. The sidekicks. Like it or hate it, Batman's 'extended family' is one of the largest and most prominent in comic book lore (if not THE largest and most prominent). One can respect Nolan's motives in leaving this one aspect of the mythos out of his series, and certainly the stink of Batman and Robin still lingers...but that's no reason why film-makers and fans alike can't give Robin, Batgirl et all another shot on the big screen. If people can accept a teenage superhero in 'Amazing Spider-Man', there really shouldn't be THAT much of a problem with a teenage vigilante 'sidekick', if done properly. I honestly feel an origin story for Dick Grayson can be the perfect way to kick off the rebooted series...and then explore Dick's evolution as Robin, and eventually Nightwing, through the span of 2-3 films. And that's just ONE of the many ways they can handle this. Again, I feel the TAS is a great template for how the sidekicks should be handled in a Batman film.