I think it was just harder to write the Prequel Trilogy... <_< Haven't you ever written anything and then decided, that there must be a story before the already written story. I know it, it's really... hard. Making the prequel lead to the original one is very hard, because all things are already decided. There should be no questions after the last sentence of the story. Even every character should have an end.
So that is why I don't think Jedi were stupid. By the way, Jedi are not supreme gods. They can sense feelings, but not like: "You love her. You killed an innocent soul!" That's not like that. They sense feelings, emotions, not thoughts and the actual thing, what led to the emotion. Yoda sensed, that something was wrong with him...
Jedi were often sent to missions alone, because they were one of the most powerful fighters in the galaxy. I have to admit, that ordering Anakin to protect Padmé was just very strange, but padawans were sent on missions too. Sometimes alone.
The Republic was actually ruled by Sidious, who had planned almost every single detail. That's why he could manipulate with everyone so easily. Of course people didn't know, how powerful Sith Lord he was, but Mace Windu acted like Jedi should. He had to kill a person, who had committed crime against the Republic.
Okay, maybe I forgot something, but that's what I wanted to say.