President Snow showed evil throughout the whole book series because he would makes is decisions based solely on his benefits. For example whenever someone would threaten on taking over his role as president he would have them killed and make it look like an accident. Another example is when he went to Katniss's house before she went on her victors tour to talk to her about making sure she proves to Penam she is truly in love with Peeta. He only had that talk with her because if Penam was not convinced with their love than it would show the Capital's weakness and an upraising could happen and destroy President Snow.
Second person that could be viewed as evil is President Coin. She made the decision to safe Katniss instead of Peeta because she knew that Katniss would have more of an impact in the rebellion than Peeta would. Once district 13 had both Katniss and Peeta and they were going to war in Capital she put both of them in the same group even though Peeta believes Katniss is the enemy and wants to kill her. Coin made that decision because she wanted Katniss to die so she would be sure to become the president if the districts would win the war.
Example of evil in the world would be a dictator. A dictator makes roles that make the people believe in him and worship him as a god. When things come down to a decision he will choose the option that will make him look better and that would benefit him the most.