I have to say, I was severely disappointed. After the fanboy hype about this movie, I was expecting a masterpiece, but only the short about Deadshot was any good (the Scarecrow short could have been better if it was longer - everything is better with Scarecrow!) and, for something that was supposed to plug the gaps between Batman Begins and the Dark Knight, it ran surprisingly free and loose with the Nolanverse canon. The artwork in most of the shorts was also rather shoddy. I have literally read better fanfiction.
Parent-wise, there wasn't any strong language that I recall or any sex - but the violence was appalling. I'm shocked commonsensemedia put it at iffy for 11+, animated or not - I'm a grown woman and I almost threw up during two scenes - in one, Bruce Wayne is volunteering in an emergency room and witnesses an extremely graphic surgery, and in the very first short when a kid imagines a vampire-like version of Batman taking an unidentified bad guy's head off - again, very graphic. Blood spatters in literally ever single story - but those were the worst two examples. Thank God these shorts didn't feature the Joker - I can just imagine how blood-drenched his short would have been. For this reason, I put it at much higher age group, and feel that, animated or no, it should have gotten a stiffer rating from the MPAA.