I think the biggest problem with domestic abuse, is that other people all too often turn a blind eye to it. They don't call the police. They don't think it's their business, so they don't get involved. They'll listen to it happen, they'll watch it happen, and they'll give you a sympathetic eye after the fact. But they don't help, and it's totally the wrong response (although I'll admit, not an easy one to change). People in abusive relationships are so cut off from their family and friends (sometimes physically, sometimes emotionally), and they may very well lie through their teeth about where they got bruises, etc. They'll probably deny that anything is wrong...at first. But if nobody reaches out to them, then they're stuck...because abuse lowers their self esteem so much that they begin to think they deserve it.
Like Lighthouse, I am also talking from personal experience. With my ex, it was a learned behaviour, from years of abuse as a child. Knowing that didn't really make it any easier on me. Passive-aggressive became verbal, which in the end became physical...which is what it took for me to get out. My neighbours knew what was going on, and after I threw my partner out, one even said she'd worried about me...but did she so much acknowledge it before then? No. My friends all told me terrible stories about things they'd heard from others about my ex...did they tell me while I was in the relationship? No. My family told me that they'd worried about me, and about the fact that I had all but cut myself off from them (not by choice)...but did they tell me that before I ended it? No. My family and friends at least were there to help me pick up the pieces of my life and get it back on track. Not everyone has that, which is why it's so important for neighbours, workmates, etc. not to ignore signs of abuse in others. Even if you don't think it's your business, GET INVOLVED! You could save someone's life.
Another problem I see with domestic abuse, is the lack of counselling - both for victims, and the abusers themselves. So many abusers were abused themselves...if they'd had adequate counselling in the first place, I believe that a lot of future violence could be avoided. Counselling and anger management don't help everyone, but it would go a long way to helping the situation.