Why could Palpatine not sense the good in Darth Vader?

Question

This question is inspired by a similar question. "Why could Luke sense the good in Darth Vader, but Obi-wan could not?"

Emperor Palpatine probably knew Darth Vader as well as anyone. Perhaps even knew him better than Yoda and Obi-wan did by the time of Empire Strikes Back. We know Emperor Palpatine can sense deeply buried thoughts and feelings within others. Why did he not know there was still some good deep inside Darth Vader?

Luke was with Darth Vader for only a few minutes of his entire adult life up to that point, yet he felt the good-vs-evil conflict within his father.

Palpatine and Vader had been together for over 20 years by that time, yet Palpatine missed what seemed obvious to Luke.

Answer 1

This is somewhat hand-waved in James Kahn's Return of the Jedi novelization:

They both knew the Force wasn't all-powerful - and no one was infallible with its use. It had everything to do with awareness, with vision. Certainly, Vader and his son were more closely linked than was the Emperor with young Skywalker - but, in addition, the Emperor was now aware of a cross-current he hadn't read before, a buckle in the Force he couldn't quite understand.

^{Return of the Jedi Chapter V}

So it seems that Palpatine was aware of something, but evidently the Force was obscuring his vision in some way; difficult to see clearly, the future is.

That being said, as you say, Palpatine is consistently well-attuned to Vader's thoughts and feelings; there's little about Vader he doesn't know. It may well be that Palpatine was aware of Vader's internal conflict, but mistook it for the same thing Vader himself did, namely a desire to supplant the Emperor and rule the galaxy with Luke at his side:

Vader felt complete at the Emperor's side. Though the emptiness at his core never left him, it became a glorious emptiness in the glare of the Emperor's cold light, an exalted void that could encompass the universe. And someday would encompass the universe ... when the Emperor was dead.

For that was Vader's final dream. When he'd learned all he could of the dark power from this evil genius, to take that power from him. seize it and keep its cold light at his own core - kill the Emperor and devour his darkness, and rule the universe. Rule with his son at his side.

For that was his other dream - to reclaim his boy, to show Luke the majesty of this shadow force: why it was so potent, why he'd chosen rightly to follow its path. And Luke would come with him, he knew. That seed was sown. They would rule together, father and son.

^{Return of the Jedi Chapter III}

This wouldn't be a feeling that Palpatine would be suspicious of; indeed, considering how Palpatine himself became Dark Lord of the Sith, he really should be expecting it.

Answer 2

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 .