After that very nice summary about Law and his character, I think I will do mine on Doflamingo.
Corazon talked about how Doflamingo was a monster, who he can't believe was born from such good natured parent. I remember the thread for that chapter, many thinking about how it takes away from his character, but after thinking about it, Doflamingo has a lot going for him. In this arc, the heart has been a heavy emphasis. Dressrosa is known as the country of love and passion, Laws fruit which Doflamingo wanted was shaped like a heart, the seat that has been empty or "cursed" is the heart seat, Doflamingo's brothers name is Corazon, and Law named his crew the heart pirates, and had Corazon on the back to remind him of the man that saved him.
The earliest we know of Doflamingo is that he was the son of a Celestial Dragon, forced to live with the common people because of his father. He was spoiled and wanted what was his, but that is minor to what was really the center of the world. From the flashback, we see that both Doflamingo and Corazon saw their mother as being very important, and when she died, that's when things started to spiral out of control. Before that, Doflamingo was shown to be spoiled, but that was it. After his mother died, he blamed his father, and showed no sympathy for him. We see him do his first terrible act of killing his father in hopes of getting back his birthright. From this, the mother was the last string of any heart Doflamingo had.
Flash forward many years. Doflamingo has created a family, one that can replace his old one. We see some sentiment he has towards them, where he saves Baby 5 and Law at one point, and isn't shown to be menacing. From everyone there though, he is most attached to Corazon, the one remnant of his old family, the only one who can understand him, that is until Law came in. Doflamingo gets attached to Law because he has a connection to him. They both suffered from people that they didn't do anything to, and the world caused them to suffer because fate had them put in situations that could've been prevented if people weren't so emotional. So while he has a family, the only two he really interacts with much is Corazon and Law.
When the two of them leave, Doflamingo figures out that he's been played. His brother by blood was with the Marines, and an inside agent to take him out. One of the last few strings holding his heart together, any humanity he might have, is broken. He goes to confront Corazon, demanding to know what happened to Law and the fruit. Corazon tells him Law and the fruit aren't his, and that Law is free. With Law free and him pulling the trigger on Corazon, the last strings of his humanity is gone. There is a void in his heart, which only the fruit could fill for him. Over time he grows in power, becomes a shikibukai, and becomes a ruthless business man. He creates a slave trade, enjoys causing his underling pain, and creates war by supplying weapons to countries.
Now we come to the Dressrosa arc, where Law returns. Doflamingo sees Law and decides that maybe he can get him to return, that everything is a misunderstanding. Doflamingo beats him close to death a number of times, but spares him because they are alike, and that Law will eventually come around. After all, Law has the power, the fruit that can fill the void where his heart used to be. Doflamingo offers him something in return for his sacrifice. He gets angry when he asks him to kiss all the citizens ass, because it should be the other way around, and it was people like his subjects that made him what he is. It would've just been Law being stubborn, until Doflamingo kicks him over to see Laws back.
Corazon and the Heart Pirates, then claiming faith in the Straw Hats. Law is exactly how Corazon described him, free from his clutches. Law admires Corazon so much, that he made his crew name in honor of him. With this, Doflamingo knows Law will never return to him, and that he took away his heart by his actions. In anger, and in a ironic way, he gives Law the "final" blow to the heart, where as with his other family, he shot them in the head. As of that shot, there will be no more mercy from Doflamingo, as the Birdcage shrinks to kill everyone in its path.