Enforced Method Acting: George Lucas intentionally put extra weight into the Darth Vader helmet so that when Hayden Christensen first walks around in the Vader suit, he almost stumbles, since Anakin/Vader's not used to the Vader suit yet.
Separated-at-Birth Casting: Tarkin appears in passing towards the end largely because they found an actor (Wayne Pygram) with an astonishing resemblance to a younger Peter Cushing and couldn't bear to not cast him!
Anakin was originally supposed to be watching the entirety of the duel between Palpatine and Mace Windu, but they realized that the implications were too subtle and somewhat confusing. This led to reshoots that has the moment where Anakin and Padmé "watch" each other across Coruscant and the duel had to be redone because Palpatine was using Anakin's lightsaber. As mentioned by a Lucasfilm executive, the original cut made it fairly clear Palpatine was playing up being helpless to get Anakin to side with him, while the reshot version made it seem that Mace Windu could have legitimately killed him, making it more shocking when Palpatine kills Mace with power that the audience honest didn't believe he still had in him.
A glimpse at the original backstory as seen in the novelization of Return of the Jedi (as well as strongly implied by Leia's lines in said film) shows us that her mother, who is now known to be Padmé, was originally meant to survive Anakin's turn to the Dark Side.
The Return of the Jedi novelization also said Anakin fell into a pool of lava. In the movie, he doesn't actually touch the lava, but the fumes are hot enough to set his clothes on fire. This may have been changed to make Anakin's survival a bit more plausible.
Star Wars: Clone Wars ended up showing the actual kidnapping of Palpatine, which was present in the early drafts of this movie but then passed over to be depicted in that series. The opening battle was originally over 45 minutes in length even after they cut out that part, including one scene having Grievous execute Shaak-Ti in front of Anakin and Obi-Wan.
There are a good amount of scenes that were not included in the final film, or even finished. These include two death scenes filmed for Shaak Tinote The Force Unleashed took advantage of this by turning her into a boss. As far as the storyline goes, both were deleted and confirmed by Star Wars Insider 87 that neither scene was canonical, and that she actually survived Order 66., Anakin and Obi-Wan treading through the sewers on Grievous' flagship, Wat Tambor's death by Darth Vader in Mustafarnote Though in the final cut, he can be seen hiding in the conference room of the factory, and images of the scene were featured in Revenge of the Sith merchandise.an entire subplot of Padmé holding meetings with Mon Mothma, Bail Organa, and other senators to plan the birth of the Rebel Alliance, and a 30-second scene of Yoda arriving on Dagobah.
According to Ahmed Best, there was a deleted scene where, before he crowned himself Emperor, Palpatine mockingly thanked Jar Jar Binks for granting him the emergency powers that allowed him to take over the Galaxy.
Lucas considered having Han Solo appear as a young boy raised by Chewbacca. Concept art for this can be found in the Art of Revenge of the Sith book and is reproduced here.
There exists concept art of a teenage Boba Fett killing Mace Windu during Order 66. Windu's killer was changed to Palpatine, as Lucas felt Boba was far too young to believably pose a challenge to a Jedi Master.
Count Dooku was originally going to survive until the midpoint of the film, with his death being the final push Anakin needed to join the Dark Side rather than Mace Windu's. His death was instead moved to the opening sequence, which had changed from its original conception (seven battles on seven different planets showcasing the fury of the Clone Wars, rather than Palpatine being kidnapped by Dooku and Grievous).
Padmé originally had a much larger role, as one of the senators opposing Palpatine's increasing accumulation of power.