Some of the most common elements are thought control, government corruption, and government oppression.
1. thought control - in a dystopian society, free thinking is often forbidden. If you are allowed to think freely, you will realize that the government is corrupted and you will want to rebel. This is why the government is trying to control what you think about, in order to keep you in check.
2. government corruption - in dystopian societies, the government is often (if not always) corrupted. Although this topic is not really different from the state of the world today, it is more drastic in dystopian novels. The government is thinking only about money, about controlling its people, and doesn't really care about the wellbeing of its people.
3. government oppression - oppression goes along with corruption. The government is oppressing its people - nobody is living happy lives in a dystopian society. Everyone is oppressed and made to do something they don't feel like doing, usually something against their will. Their minds are also often controlled so that they don't understand that something is wrong - but there is always someone, at least one person, who is different and who will try to wake people up and fight the system.