Well, lets start with two quotes . One is from Master Yoda, about Dark Side:
Recognize you, I do. Part of me you are, yes, but power over me you have not. Through patience and training, it is I who control you. Control over me, you have not. My dark side you are, reject you I do.
Other is from Solzhenitsyn:
Gradually it was disclosed to me that the line separating good and evil passes not through states, nor between classes, nor between political parties either -- but right through every human heart -- and through all human hearts. This line shifts. Inside us, it oscillates with the years. And even within hearts overwhelmed by evil, one small bridgehead of good is retained. And even in the best of all hearts, there remains ... an unuprooted small corner of evil.
Sith did consider what we know as Light Side and goodness simply as weakness. You are good because you are too weak to gain power and to use it. Mercy, compassion, friendship ... these are all chains that prevent full freedom that could be attained only by embracing Power of Dark Side.
Yet, perfection does not exists - even in blackest heart there were some traces of Light. We could argue that even Palpatine, embodiment of Dark Side, did somewhat care for Vader and that is the reason he saved him on Mustafar. Ironically, Vader as his weakness cost him his life. Son, another powerful Force user embodying Dark Side, genuinely cared for his sister Daughter etc ...
From Palpatine's perspective, Darth Vader was far from ideal Sith. Vader suffered from remorse, blamed himself for Padme's death, and Palpatine correctly sensed conflict in him . But, that was nothing new for Palpatine. Vader, and before that Anakin, was always full of contradictions and conflicting feelings. And yet, Palpatine always managed to resolve those Anakin's internal dilemmas to his advantage : killing of Dooku, killing of Mace Windu, slaughter of Separatist leadership, even conflict with Padme on Mustafar.
So Palpatine did sense good in Vader, only he failed to realize it would triumph this time . Reasons for that are debatable, most likely because Palpatine never before that moment directly attacked someone for whom Anakin really cared .