Since most people think that Norman Osborn is dead and that Spider-Man killed him, Jameson's tirade against Spider-Man (who he already has a beef with because he blames him for his son's incarceration at Ravencroft) goes into high gear, with Harry being propped up as well as the "grieving son." Mencken, no controlling Oscorp, along with Jameson using the Bugle as publicity, and Miles Warren as the head scientist, hires Mac Gargan to become the Scorpion to be the perfect oppontent against Spider-Man--which of course results in an even bigger mess.
This could be part of an overall story arc in which Oscorp and Miles Warren privately hire or create oppontents to take out Spider-Man, with Jameson's offering a reward for Spider-Man's capture. This could include, along with the Scorpion, the introduction of the spider-slayers, and the creation of Hyrdo-Man. Or maybe, it could also result in the Sandman as a "hero for hire" to bring in Spider-Man for Jameson. Or maybe the Black Cat seeking revenge against Spidey for allowing her father to stay behind in prison.
Likewise, because of the power vaccum in organized crime that's been created, someone is raiding all of the Green Goblin's stashes and has taken up the mantle of the Hobgoblin, thus creating another story arc. Suspects include Roderick Kingsley, Daniel Mencken, the newly released John Jameson, and even Harry Osborn. This, eventually paves the way for Norman Osborn to return to try and stop however is stealing his Goblin equipment. It also allows for folks like Silvermane, Tombstone, Hammerhead, Silver Sable, and even Doctor Octopus to get back into the action. Likewise, this could also be the arc in which Norman reveals to Spider-Man that he knows he's Peter Parker.
One running subplot through the series could be Peter, believing that he's lost Gwen to Harry, decides to do his best to get over her and move on, ends up becoming closer to Mary Jane, who because of Mark becoming the Molten Man, is having her own share of the romantic blues. This becomes complicated when MJ finds herself seeing Peter as more than a friend and falling in love with him, even though Peter sees her as just a "really good friend" and is still in love with Gwen. And it becomes more complicated when Peter and Gwen have a chance to get back together and MJ, not wanting to hurt Gwen's feelings or impede on Peter's happiness, can't reveal the truth. Furthermore, she later discovers that Peter is Spider-Man.
And since this season would be the end of a school year and that they would be off for the summer, it also could be an opportunity for their version of the "Death of Captain Stacy" story, with Captain Stacy revealing that he knows Peter is Spider-Man after being critically wounded during a fight between Spidey and Doc Ock. This further complicates matters between Peter and Gwen again just like in the comics, since Gwen would blame Spider-Man for what happened to her father and also prompt her to go visit relatives in England over the summer with the question of her coming back in doubt. This could also result in a "Spider-Man No More" homage, which is how MJ learns he's Spidey after finding the suit in the trash.
One interesting idea could be that Miles Warren ends up experimenting with the inmates at Ravencroft, especially when it comes to Electro and Eddie Brock since both of them had close connections to Dr. Connors and that he manages to find the Venom symbiote--not to mention homeless people who show signs of infection. This then results in a "symbiote infestation arc" which includes Cletus Cassidy as Carnage, and Spidey and Venom forced to team up in order to keep the symbiotes from spreading. It also could lead to the basis behind a possible cloning of Spider-Man as in the classic Gerry Conway story.