These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Lucas may have retconned the George W. Bush reference since the film was made during the 2004 elections but released afterwards. Lucas only denied that it was anti-Bush after President Obama was elected, who Lucas supports but who has many similar policies. In particular, Anakin's phrase "If you're not with me... then you're my enemy." is a reference to (one formulation of) the Bush Doctrine that countries that support terrorist groups are treated as if the terrorists are acting on their behalf. (It's also a re-phrasing of the classic liberal political saying, "You're either part of the solution, or you're part of the problem.")
It's also been noted that Palpatine's rise to power has more in common with that of Caesar Augustus, Napoleon Bonaparte, or Adolf Hitler.
Broken Base: The worst out of all of them. The main issue being Anakin is either an effective Tragic Hero whose fall to darkness is simultaneously tragic, terrifying and Badass, or the same old poorly-acted Wangstyromantic he was in the last movie.
Complete Monster: Palpatine. Add-on materials including the novelization reveal he was angry at Anakin for losing to Obi-Wan and considered leaving him for dead since he was crippled both physically and in his strength with the Force. The only thing that convinced him otherwise was that Anakin would still be powerful even in this state. On the other hand, in the movie he seems only to be impressed that he was alive, and isn't angry at all. He also did much the same thing with General Grievous— manipulating him into being horrifically crippled so that he could be re-built into a super-cyborg monster.
Contested Prequel: Like the other two prequels, though leaning more towards the positive end of the spectrum.
Critical Dissonance: Gets enough flak from fans that its Rotten Tomatoes rating of 80% might surprise some people, especially considering this is just barely higher than Return of the Jedi's 79%.
Many critics erred on the side of trashing the original trilogy, and modern critics would rather err on the side of what would have seemed to have been a sure thing.
Fanon: Many fans like to believe that Darth Plagueis' life-creating experiments caused Shmi Skywalker's unexplained Mystical Pregnancy, and that Anakin has abnormally powerful Force abilities because he's essentially a Human Weapon created by a Sith Lord.
Fight Scene Failure: The Palpatine/Windu fight looks rather pathetic, due largely to Lucas' insistence that the elderly Ian McDiarmid do it himself instead of using a stunt double and digital face like they did for the Dooku/Yoda fight in Attack of the Clones.
Somewhat josssed in the sense they did use a stunt double for Ian Mcdiarmid. They had to use him in the close up and mid shots.
The already horrific multiple-murders of Order 66. If you've watched Star Wars: The Clone Wars or read any of the EU material, every Jedi they show getting murdered has gotten screentime and lines, which is more than you can say for the movies. They're that much more alive, and their deaths are that much worse.
Dave Filoni (The supervising director of The Clone Wars) admitted to being under this effect in regards to minor character Plo Koon due to being his favorite minor Jedi in the EU and even going to the movie dressed up as him. Talk about a Tearjerker...
For another The Clone Wars-related example, Season 6 reveals how Order 66 works, and all from a clone's perspective. After watching that story arc, the Jedi who were killed aren't the only ones you'll grieve for. Even harsher, an interview about Rebels revealed that some of the clones who survived the Clone War (particularly the ones that served closely with their Jedi generals) are now suffering PTSD over it.
Not that it was pleasant beforehand, but the prospect of Anakin massacring young kids became way more uncomfortable after the Sandy Hook massacre.
He Really Can Act: For a few minutes when he has no lines as he begins the massacre of the Jedi Temple, Hayden Christensen is genuinely scary looking as a dark-sided Anakin, now Darth Vader. While this is also a polarizing performance, many fans who don't hate the film point out how the way Hayden Christensen acts is a lot more appropriate than in the previous film, where it was more narmy.
Was claimed Mace Windu and Aayla Secura, even though they're both killed onscreen. Mace's survival is at least somewhat plausible. He loses his hand, gets zapped by lightning, and tossed from a significant height, all of which Jedi are shown to be able to survive throughout the saga (although never all at once.) Secura however, gets shot in the back by at least a dozen troops at near point-blank range, and her body continues to be shot as the camera pans out.
After the announcement of The Force Awakens, a lot of people began to apply this train of thought to Darth Plagueis, based on Palpatine's comments that his old master was able to conquer death. The Tarkin book dropped a couple of details about the enigmatic figure into the canon also helped the theory gain some support. A number of people are convinced that he was somehow Faking the Dead and could be the Big Bad of the Sequel Trilogy as a way of raising the stakes from his apprentice.
Much of the reason Anakin loses trust in the Jedi and eventually betrays them is due to them not trusting him, thus giving him good reason to do the same. In the end, Anakin's betrayal of the Jedi was as much them pushing him away as him turning his back on them.
Also, Anakin's (and the rest of the Jedi's) failure to spot the obvious - that Palpatine was the Sith Lord. He was almost amazingly athletic during the escape from the Invisible Hand, especially for an aging politician. Then there was his creepy storytelling at the opera house. (So...it never occurs to Anakin to wonder exactly how Palpatine knows about that "old Sith legend"?) Finally you have the simple and obvious fact that he was increasingly dictatorial. It was really kind of glaring.
Magnificent Bastard: Palpatine. He plays every single character in the movie like a fiddle and becomes dictator of the galaxy by the end of the second act, and by the end of the movie all of his potential enemies are either dead, on the run or on his side. Granted, at least part of this is because some of those enemies are not always the brightest folk, but they suspected that something was wrong with him being in power so long and thought at the very least that the Sith might be controlling him, and he still covers his tracks until its too late for them.
Memetic Mutation: Vader's "NOOOOOOOOOOOOOOOO!!!" has since been used as a way (mostly in jest) to show great disapproval over things on forums and message boards.
The NO part also spawned a different famous meme thanks to a cheap chinese bootleg of the movie having horribly translated subtitles in English. During the scene the "no" was translated as "Do not want!" which quickly became a reaction comment towards unwanted things or gross images.
"You underestimate my power!!!"
"Only a Sith deals in absolutes."
"You were the chosen one!", usually in rage comics to show betrayal but full variations of the quotation have been made◊.
Also because some like to note that it's odd for Obi-Wan of all people to say this, since he himself overcame this disadvantage against Darth Maul in The Phantom Menace. Though, to be fair, Obi-Wan was smart enough to exploit his advantage, whereas Maul wasn't.
When Anakin has Count Dooku at his mercy, Palpatine implores Anakin to kill him in a very forceful way, specifically using the phrase "DO IT!" fiercely. After Game Grumps made fun of the scene (showcased throughthesevideos), it's hard for one to take it seriously.
Moral Event Horizon: Palpatine crosses it when his begins the Jedi Purge. Anakin appears to cross it when he kills younglings, but anyone who has seen Return Of The Jedi knows that he ultimately redeems himself in the end.
In the Mace/Palpatine fight, immediately after Mace kicks Palpatine's lightsaber away, there's a hilariously dull shot of Anakin running at a rather casual pace, made even worse by that it doesn't at all match the tense music that's playing.
"Anakin... has killed... younglings." Child murder is horrific in and of itself, but the word "younglings" either spoils the mood or makes it feel less like the real world and more like Star Wars.
Natalie Portman is a good actor, but even she can't make a clumsy line for her character's anguish, "Anakin, you're breaking my heart." sound anything but stupid.
The whole "You're so beautiful." banter between Anakin and Padmé. It was so terribly written that both Christensen and Portman seem to be uncomfortable reading those lines.
"I HATE YOU!!!"
Nightmare Fuel: Anakin/Vader's transformation from man into human-machine hybrid. Word of God has stated that he was not on any anesthetic, so he was awake and in horrible pain the whole time he was being placed in the suit.
During the fight when Count Dooku drops part of the walkway on top of Obi Wan, it looks really fake. Obi Wan was just moved down on the screen when it fell on him without any of his limbs reacting to the impact.
Palpatine's backflip during his fight with Mace is also rather unconvincing.
When Grievous is getting his lightsabers out in front of Obi-Wan, it's pretty easy to tell that Ewan McGregor is looking at a green screen the whole time, as he shows little reaction to this and keeps his guard down the whole time, just awkwardly standing there. He doesn't even flinch when Grevious waves the lightsabers dangerously close to his face.
Surprisingly Improved Sequel: Most fans agree that Revenge of the Sith is the best of the prequel trilogy. Some fans even consider it to be on the same level as The Empire Strikes Back in terms of quality.
Uncanny Valley: During the Mace/Palpatine fight, there's a couple of shots where Palpatine is completely rendered in CGI, and it's quite noticeable.