Bingowings said:

I don't know how much this could be done but maybe instead of having the water-ball ballet at the Opera House in ROTS, there could be a propaganda piece about how the evil Jedi Dooku had started the war and was defeated by the efforts of the Grand Army and The Chancellor.

It would show how the regime was already twisting the story against the Jedi and in favour of Palpatine and serve as a better parallel to Palpatine's grooming of Anakin.

^Agreed.

A real missed opportunity is that Palpatine could have insinuated that it was the Jedi behind the war. He could have suggested Dooku was colluding with the Jedi council to perpetuate the war, and they used it to build their power to take over the Republic. The Sith were just a proxy on which to place blame. What about the mysterious Jedi that supposedly ordered the clone army? It seems such an obvious thing to do.