Not. My. Problem.
Also, I think there's a little more to it than this, usually. Only sociopaths actually think this way, and most people aren't sociopaths. As cynical as I am about the state of society, I think that there are a minority of truly bad people in the world, but social structures enable and have made those people really really good at taking advantage of common psychological quirks to occupy the majority of the world's positions of power. When you look at things this way, they actually make a lot more sense.
More common than "Not my problem" is, I think, the Bystander Effect. The more people involved in a situation, the more likely each person is to assume that someone else is going to take the lead in addressing it. In the end, this amounts to nobody doing anything, and the realization not hitting until it's too late. Example: I haven't looked at statistics on it, but I'm pretty sure it's been widely observed that a lone witness to a crime or person in danger is incredibly likely to offer help. On the other hand, when such things happen in front of a large public crowd (and proportional to the size of the crowd), it's most common for people to wait until the last second to take action, or not at all.
The effect is magnified in most situations, but especially when it comes to large scale social issues, when the first person to take action invites special responsibility or consequences on themselves. Most people would be willing to do so if they knew that it was solely up to them... but they hold on to the hope that someone else will get the ball rolling first.
In my own workplace, I've talked to almost everybody. Not a single person is happy with this job. Everyone agrees we're treated like crap, in some cases to the extent that we're not even sure of the legality. Everyone understands that if we took organized action that it could all be turned around pretty quickly. But who's going to take the lead? Whoever initiates action will be fired. Period. They couldn't fire everybody, but they would sure as hell make an example of someone. In my new hire training 8 years ago, they even straight out told us that anybody involved in a unionization effort will be fired. They'd probably be blacklisted from most future employment opportunities, too, since most employers contact previous employers and take their accounts very seriously when hiring. So who's going to put their neck out, and sacrifice themselves to improve things for everybody? I'm just as guilty as anybody. I think the only difference between me and most people is my level of self-awareness about it.
I'm sure there are similar forces at work among police. I know there are police who agree with the Occupy movement or are disgusted by the actions of corrupt officers who criminally abuse their power. They'll even talk about it in interviews, but... when it comes to action, they'll buckle to pressure. When they're in their riot gear, they'll do whatever keeps their job another day. They can wait a little bit longer for someone else to say no first. The guy who takes it upon himself to begin the shake-up of that institution from the inside will have to deal with some severe shit, I'm sure.