I was shocked to realize after watching episode 1 that some people don't understand that Darth Sidious and Senator Palpatine are the same person. This seemed obvious to me from the movie. Here is why:

1. Darth Sidious never appears outside Coruscant except by holoprojection. Neither does Palpatine.

2. Darth Sidious said to Darth Maul, "I have the senate bogged down in procedures." How better to control them than by being an influential member of the senate himself?

3. Palpatine said to Anakin, "We shall watch your career with great interest." There is no reason for him as a politician to do this, but Palpatine is planning on keeping his eye on Anakin as a possible apprentice.

4. When Palpatine became Emporer, he was a master of the dark side of the Force. However, Senator Palpatine does not seem to use the Force at all. Darth Sidious does. Darth Sidious is an identity in which Palpatine can use the Force without attracting attention. He could keep his abilities hidden until he becomes Emporer, then when he makes them known nobody will get mad because he's, well, Emporer.

5. At the end during Qui-Gon's funeral, Mace Windu and Yoda have a conversation about the sith. Yoda says, "Always two, there are, a master, and an apprentice. No more, no less." Mace Windu responds with, "Yes, but which was killed, the master or the apprentice?" At this point the camera zooms in on Palpatine who is sitting nearby. The music hits an ominous sounding note. I think this may be some foreshadowing of things to come.

6. They look alike.

7. They are both played by Ian McDiarmid.