At the end of Revenge of the Sith (Warning: This question is obviously full of spoilers), when Darth Sidious stands near Vader in the surgery lab, there is this small, but quite important dialog between the two I always had a problem with. According to the ROTS script:
DARTH VADER: (continuing) Where is Padmé? Is she safe, is she all right?
DARTH SIDIOUS: I'm afraid she died. ... it seems in your anger, you killed her.
This implies that Darth Sidious did know about the argument between Vader and Padmé on Mustafar. Even more, he knew that Vader tried to kill her. But how did he came to know that? He was not there when they met, and even Vader didn't know Padmé was about to visit him.
Does Sidious even know about how the relationship between Vader and Padmé developed in those last days? Actually, Padmé did change her mind in relation to Vader just at this moment on Mustafar. Even Vader himself did not know about (or recognize) her true feelings until that climatic point. There was no sign that suddenly, Vader would try to kill her.
So even if Sidious had complete control over Vader and was able to read his mind (I don't think he was able to do so, or was he?), he didn't have any information at that point about: (a) their argument on Mustafar and (b) that Vader did actually even try to "kill her in anger".
So: How did Sidious get this information? Is there any canonical information I have missed?