A lot of the romance subplot actually begins to make sense if you interpret Anakin as (un)intentionally using the Force to manipulate Padmé's emotions, causing her to fall in love with him. This isn't actually too far out there; it's not like we haven't seen that even more well-balanced Jedi (like Qui-Gon and Obi-Wan) will casually use their power to mess with people's minds in order to get what they want.
Though the EU (especially the comics) don't take it as far as Mind Rape, they clearly present Anakin's obsession with Padmé as extremely unhealthy, possessive, and dysfunctional. What is unclear is whether or not Lucas intended to imply this interpretation, or whether he was genuinely trying to write them as a romantic couple and that somehow fell through.
Alternatively, the awkwardness of the scenes also makes sense when you realize how incredibly sheltered Anakin and Padmé's lives really are. Neither of them had any real relationship experience before - aside from Padmé's brief summer fling when she was about twelve - and would have no real clue what they're doing. This would also explain how they never really looked past the hormonal fog and shared history to realize that they weren't really emotionally and mentally ready for a long-term relationship, never mind marriage.
Why she seems to somehow forget what Anakin did to the Sand People, including killing their children, between him telling her this and when he murders the Jedi Younglings in Revenge of the Sith. Though to be fair, a great deal of time passed between movies two and three, during which the Clone Wars raged. While it would seem hard to believe she completely forgot what happened, it can't be denied there was likely a lot on her mind prior to the attack on the Jedi Temple. Or perhaps, like everyone else, Padmé just assumes that the Sand People are nothing but savage cannibals who go around brutalizing people for fun and thus viewed them as not deserving sympathy; an assumption that's hard to argue with after Anakin brings back his mother's heavily tortured corpse.
Some fans suspect that Yoda training all Jedi as children was thrown in to fix the continuity issue of Qui Gon being Obi Wan's master in the last film, when he'd called Yoda "the Jedi Master who instructed me" in Empire Strikes Back.
Jango Fett's prominent role in this film was most likely put in to appease fans who complained about the Ensemble Darkhorse Boba Fett being tragically underutilized in the Original Trilogy, and getting almost no action scenes despite being built up as a Badass. Note that Boba is established as an exact genetic clone of his "father" Jango, meaning that Jango is Boba Fett, for all intents and purposes. Unlike his "son", he gets an elaborately choreographed showdown with a Jedi Knight, a space battle, and an appropriately epic death scene.
Lucas apparently finally recognized Boba Fett's massive popularity with fans, so he retroactively gave the character a much more important role in the story and gave us Jango Fett, his father/clone who looks and dresses just like him but actually gets several awesome action scenes.
Jango's bounty hunting partner Zam Wessel was also a popular character, despite her limited screentime.
Among the Separatists, Wat Tambor is uniquely beloved for his funky retro-future design and distinctive voice. Befitting his popularity, he was given a role in Star Wars: The Clone Wars.
Christopher Lee as Count Dooku, Ian McDiarmid as Palpatine, Oliver Ford Davies as Sio Bibble and Silas Carson as Ki-Adi Mundi and Nute Gunray all in due part to their performances, even if one of them is non-speaking.
Kit Fisto was very popular among the Jedi featured in the Arena battle for his unique look and cheesy grin, and like so many Ensemble Darkhorses from the prequels, was given an expanded role in the cartoon.
Anakin's guilt over murdering the children of the Sand People becomes extremely disturbing after the next movie, in which we see one of his first deeds after turning to the dark side is killing younglings at the Jedi temple.
Also Anakin, when complaining of his nightmares, says he'd much rather dream about Padmé. When you know what happens in the next movie...
Romantic Plot Tumor: At least to some degree between Anakin and Padmé. Probably made more glaring by some of their scenes having toe-crunchingly awkward dialogue. While by no means the worst tumor in film history, being a Star Wars film is the reason that the trope was originally called "George Lucas Love Story".
Rooting for the Empire: Actually encouraged by George Lucas. The movie introduces the sympathetic Clonetroopers, who save the Jedi and rout the movie's villains. Then comes the finale, and the movie reminds the viewers that they had been rooting for what will become The Empire by playing the Imperial March.
So Bad, It's Good: Hayden Christensen's acting, especially when he has to be romantic.
During the scene where the Kaminoans are showing Obi-Wan the clone army, there's a shot of several dozen clones eating in a cafeteria. The plates they are "eating" from do not actually have any food on them. They attempted to obscure it by placing a bowl in front of the center clone's plate, but it's obvious there's nothing behind it, and you can also see the empty plates of the clones on his left and right if you look fast enough.
Obi-Wan's beard has a tendency to look fake in certain scenes.
The CGI as a whole is often a point of criticism when it comes to the movie. As it's both overused and, by large, cheap-looking and ugly.
Take That, Scrappy!: Lucas finally admitted that Jar Jar was a horrible character, and in making him responsible* sort of; the plot point was going to happen regardless, Jar Jar just sped it up for enabling Palpatine's rise to totalitarian power, just wanted to give viewers one last reason to hate him. He later had a statue put up in his studio of Jar Jar frozen in carbonite, so at least he can laugh at himself.
An assassin who's also a shapeshifter? Awesome! (And also hyped in the pre-release publicity.) Sadly, Zam Wessel's ability to change her appearance is never actually used in any way whatsoever, even in a crowded bar where it would seem that looking like someone new (and taking your distinctive headgear off) might help you approach your targets. It was evidently more important to recreate the "disarming" from the Cantina Scene in Episode IV.
Luke's Uncle Owen and Aunt Beru from A New Hope first appear here chronologically, but they're barely in the film. Owen is established as Anakin's stepbrother, but the story doesn't allow them to form any sort of bond, much less establish a reason as to why Owen and Beru would be willing to take care of Luke later on, considering their only interactions are informing him that his mother's been kidnapped and grieving briefly with him at her funeral. This also contradicts Obi-Wan's account in A New Hope where it seems like the two had a long history together.
Uncanny Valley: Seen Temuera Morrison? Cool. Seen a million Temuera Morrisons in CGI? Yeah.
Considering the nature and purpose of the clone army, one could make a case for it being an Intended Audience Reaction - a million-strong Temuera Morrison army is never going to not be Uncanny Valley, and considering the dubious origins of the army and their eventual hand in eliminating the Jedi, taking advantage of the Uncanny Valley to highlight that there's something off about all of this seems to be a feasible thing to do. Evidence for this is included in the visual dictionary regarding the blanker stare of the troopers.