Dark - as in serious, dangerous, with heavy doses of hopelessness and pessismism. In other words, like Batman is supposed to be. Don't know what the movie got, but it should get an "R". It's not a kid's movie. It's not a kid's Batman or a kid's Joker. And yet, a child's logic cuts directly to the chase - there are such evils out there than the only solution to them is a controlled, measured evil - if such a thing exists - and in such a case, that must be "good."
Think of the Batman who, in the first movie, said in response to a criminal saying, "I swear to God!" replied, "SWEAR TO ME!" That's dark. That's the terrifying character that Batman is supposed to be.
And in this movie, his adversary is something even DARKER - something very close to the border of what we can realistically consider human on only our most generous of days - the kind of evil that makes everyone around agree - even the most liberal of liberals - all agree, "Kill it." ("it" chosen purposely, rather than "him.") Something beyond savagery - something utterly without conscience, and perhaps even without soul.
That's what we're talking about when we say "Dark."