If you want to produce a brilliant sequel, hire the same people who made the first movie: Sam Raimi to direct, Danny Elfman to write the music, John Dykstra to do the effects, and actors like Toby Maguire, Kirsten Dunst, James Franco, Rosemary Harris, and J.K. Simmons to play in it. And if it's a superhero movie, get someone like Alfred Molina to play one of Marvel's greatest villains.
Peter Parker (Toby Maguire) still can't get a break. He's got a job delivering pizza, but he has to deliver them as Spider-Man because he's always being delayed saving people's lives, and he is fired. His other gig photographing Spider-Man for J. Jonah Jameson (J.K. Simmons) at the Bugle is not doing well either. His grades are declining, the rent is overdue for his crappy apartment, Aunt May (Rosemary Harris) is losing her house, he washed his clothes with his Spidey outfit and the colors ran, his best friend Harry (James Franco) still wants to kill Spider-Man, and he's afraid to tell Mary Jane (Kirsten Dunst) that he loves her. He stopped to save people in a police chase and the mean usher (Bruce Campbell) wouldn't let him in to see Mary Jane's play, so he waited outside, only to see her with her new boyfriend.
This would be enough to drive most heroes to super-villainy, but he just loses his powers, intermittingly at first and then altogether. He tosses his Spidey costume away, as in "Spider-Man No More," probably the most famous Spider-Man comic. A trash-picker sells it to J. Jonah Jameson, who mounts it on the wall like Han Solo in Carbon-Freeze.
Meanwhile, Doctor Otto Octavius (Alfred Molina) works for Harry Osborne at Oscorp and since Peter wants to interview him for school, Peter is invited to the unveiling of the scientist's new Waldo-like cyborg tentacles, handy for handling dangerous substances like tritium and generally messing with nuclear powers that ought not to be messed with, and a tour-de-force of the art of special effects. The four tentacles clearly have different personalities and Alfred Molina named them Harry, Larry, Flo and Moe. Flo, he believed, was female because she was always fussing with his attire.
Something, of course, goes horribly wrong. Doc Ock's wife is killed, the arms are fused with his nervous system, and the chip that allows him to control them instead of vice-versa is destroyed. They kill all the doctors trying to separate the arms from his spinal cord and he escapes. He is the perfect villain for Spider-Man to tangle with: a megalomaniac with a brilliant mind and robotic strength, able to climb buildings and confront Spidey in his own territory--the towers of New York. He has always been one of my favorite villains.
Like all ambitious bad-guys, he begins by robbing banks--in this case the one where Peter Parker is trying to get a mortgage loan for Aunt May, and she is taken hostage. Her rescue is one of the three great battle sequences of the movie. The second is the battle atop the speeding elevated train, with the Chicago El pretending to reside in Manhattan. The third is the climactic confrontation in Doc Ock's collapsing waterfront lair, where Spidey has to stop Octavius, rescue Mary Jane, and incidentally prevent all of Manhattan from being sucked into a black-hole-like void.
Throughout, there is more than shock and awe for the audience. We are angered by the way poor Peter is treated, rejoice when Spidey is supported by the people, and find ourselves touched by Aunt May's and Mary Jane's stubborn love for him. Oh, and the famous kiss from the first movie is a plot-point.