In "Return of the Jedi" Palatine roots for the good guy again, he urges Luke to finish Vader off.

Palpatine was hoping to see the end of Dooku so he could get to his new apprentice: Anakin.

But he's urging Luke to turn to the dark side...tempting him. What gets me about
that scene is that no one is around to see who Palpatine is rooting for....it seems a
little strange to me, but I guess that is the only explanation.

Perhaps it's thrown in there for the audience members that have never seen any other episodes. If they see Palpatine cheering for the good guys in the beginning of the movie, it will be even more of a shock to them when he reveals that he is a Sith.

Plain and simple; he was rooting for the good guy's because he wanted the good guys to win. Dooku had served his purpose, and it was time for him to go; I think Palpatine was hoping that Obi-wan and Anakin were going to kill him. Also, if Dooku had won, Anakin would have been killed; and we've seen from novels (e.g. Outbound Flight) how protective Palpatine was towards him. Palpatine was already planning to try to turn Anakin to the Dark Side, and it would have been a major blow if his prize had been killed before he had the chance to set to work on him.
Just my thoughts....

Good question.
Like everyone else said, Palpatine wanted to see Dooku's end. And he knew that, if he cheered the Jedi on, they could easily do it. And they did.
BTW, I do believe that when Obi-Wan killed the two super battle droids, Palpatine said:
"Get--!" Maybe he was about to say, "Get Dooku!" or, "Get Dooku from both sides!" and just thought better of it, so he stopped himself short. But anyway, it could have been "Yeah!", but that's what I heard. I'll have to check the subtitles later.

Palpatine said:
"Get--!"

Actually, he said "Yeah!" or "Yes!" (can't remember exactly which one)


If you don't mind my throwing my two cents in and reiterating what's already been said, yp4, Palpatine knew Dooku, though strong, had to die, hopefully by Anakin's hand. It would be one more step along Anakin's journey to the Dark Side. Anakin always was the apprentice Palpatine was after. Why not root for the heroes?

MTFBWY

Palpatine had to seem good and it probably wasnt conveinient to have Ani or Obi killed. But later palps wanted to leave obi. Whats up with that? Oh and Ani is right that Obis fate was the same as thiers: All 3 died on board a death star.