For several years after Star Wars The Phantom Menace was released, I just couldn't see what was so horribly wrong about it, and why people hated it. The subsequent two movies were quite ok as well.
Now, don't get me wrong. Back then I thought that the vast majority of people hated it simply because the vast majority of other people hated it, and it was just a hip and cool to hate it (a phenomenon I have complained about several times,) and I still think that's mostly the case. However, I have later come to realize that some of the criticism of the prequel trilogy is, indeed, valid. I have come to realize that my own appreciation of the trilogy has dropped significantly since those times.
What changed my opinion the most was the great review series done by The Distressed Watcher (who I think made a terrific job at analyzing it, and sadly has gone mostly unnoticed by the vast majority of people, who only know the review by Red Letter Media which, while funny, I don't think is as good.) He presented a lot of good points that I just have to agree with.
And still don't get me wrong: I still don't think the prequel trilogy is the worst pieces of movie that has ever been made. They are still in the mediocre category for me. Also, I don't hate Jar-Jar. I'm sorry, but I just don't.
Anyway, one of the major problems with the entire trilogy is that it's supposed to be the story of how Darth Vader came to be, of how he changed from a good person to a mass-murdering villain of galactic proportions, yet the trilogy spends surprisingly little time showing (or even just telling) about it. By far the vast majority of the time is spent on other things entirely, mostly things that have no effect on that core plot.
The problem with this scarcity of background story is that Anakin's change in the end comes way too "easily." There's very little that would explain why exactly he decided to switch to the other side, and moreover did it in such a drastic way (eg. one of the very first things he did after he switched to the dark side was to personally massacre a group of children; off-screen, mind you, but clearly implied.) With so little background leading up to this radical change, it kind of comes a bit out-of-nowhere, with no explanation. There are bits and pieces during the second and third films yes, but way too little. And what's worse, even the little there is, is written in a simplistic, even childish manner (like something that a 12-year-old would write.) This is quite obnoxious given that, as said, the core plot of trilogy is supposed to be exactly this.
Anakin in the first movie is an archetypal Mary Sue character: Perfect, pure, innocent and "cute" in all possible ways, with no flaws. While this kind of character can work when well done, it was not very well done here. He's not very likeable nor relatable, and many people could understandably even consider him annoying. By being too perfect, too innocent, too cute, what's clearly intended to be a likeable and endearing character only ends up being a two-dimensional portrayal with no depth to him at all. I'm assuming that what Lucas was attempting is making the viewers love the character, making his fall that much more shocking and sad, but he just outright fails at this.
While Anakin's conversion to Darth Vader was (supposed to be) the core plot of the trilogy, another almost as relevant plot point was his fathering of Leia and Luke Skywalker. In other words, the romantic subplot of him and Padme Amidala.
Quite incredibly, this was handled as poorly as the main plot. The romantic scenes are scarce and brief, and most damningly, extremely badly done. There's absolutely no chemistry between the two characters, and watching these scenes is just uncomfortable. As the Distressed Watcher puts it, it's like watching two people who feel absolutely nothing for each other forced to act in romantic scenes. While this is of course subjective, you just can see that their heart was not in the acting, and you feel like they are just doing their job to earn their salary. (This is something that a good director should catch and fix, by whatever means. The fact that Lucas did not fix this tells us something.)
Lucas was clearly trying to write the subplot as Padme denying her feelings for Anakin for a long time, and slowly warming up, but it just doesn't come out like that. Instead, it comes out as Padme repeatedly rejecting Anakin, who ends up looking more like a stalker with an obsession, with almost childish qualities. (Again, something that a good director ought to notice and fix.) Overall, the entire subplot is very poorly done and painful to watch.
Padme's reactions to many of Anakin's doings is also quite unrealistic. For example, when Anakin confesses that he massacred an entire village, women and children included, in a rage to revenge his mother, Padme acts like he had just told her that he lost his wallet.
And as a side note, Lucas deciding to kill the absolutely best character of the entire trilogy at the end of the first movie was just a huge mistake. Darth Maul is possibly the only character in the entire trilogy that nobody hates, and almost everybody agrees was the coolest thing. Killing him in the first movie was just a bad, bad idea. Lucas completely lost the ball with that one.
And that big "no" at the end? Yes, Lucas completely lost the ball. Completely. If people are laughing in a scene that's supposed to be extremely dramatic, something is really, really wrong.