Growing up in school I would see bullies. Many of these bullies would be spoiled kids of rich parents. In fact, I've seen this trend where the more rich and affluent a family the more spoiled and insensitive their kids grow up to be.

You can even see examples of this among politicians, movie directors, the famous drunk driving kids of MLAs who get away with doing such evil things.

We typically say that the law of karma has caused such people to be born rich. 

However, after being born so rich, these people have been committing crimes for decades in their lifetime while the poor people who grow up in a harsh environment turn out sensitive and caring?

We can see this pattern among world leaders as well who suppress their citizens and take away many of their freedom rights. 

If you must do good deeds to get wealth and power in your next. We also say that the progress that you make towards dharma carries onto the next life. If that is true then how come so many people in wealthy families commit the worst of crimes?

TL;DR: People do lots of good deeds, get born in wealthy and powerful families. Then they do a lot of bad, insensitive things and end up harming lots of people in masses. 

How have they made any progress in life if the law of karma is really valid here?