The greatest failure of SM3 was the mismashed storyline. It was written to be Sandman and Vulture... whatever the studio wanted, they should have made that clear in the beginning so that the proper focus could be given. Don't say, "hey, we know you've already written a script, but now we want venom in it. Can't you fit him in there somewhere?". The end result was getting a lame venom origin with an underwhelming use of the black-outfit and Venom as a unique character. Sandman feels unnecessary and out of place as well. Throw in the Goblin storyline and nothing quite gels at all (even though they attempt to justify it at the end with a team-up).
Here's how you make the story work better:
• use John Jameson to help introduce the symbiote (a la the cartoon). You've already introduced the character in the previous friggin' movie... why suddenly pretend he doesn't exist?
• keep the Goblin storyline basically the same... the build-up works and keeps the flow from previous films.
• Have spider-man spend more time as the focus of the movie, converting into the black-suit much earlier. Have it work as an organism, not just a dye-job on one of his suits. (i.e. show the suit morphing onto his body from his street-clothes.)
• develop a transition from "cool new toy" to "power-struggle" with the alien symbiote. Show how it is affecting Peter's personality.
• Show a lot of day to day Spidey scenes using the black suit. He's tougher, but also rougher with the street baddies. People don't like that he seems "mean". Popular opinion turns against him.
• Have him figure out that sound waves harm the symbiote with the help of 'biologist' Dr. Connors.
• Build a better rivalry between Brock and Parker so we believe it when Brock hates him and wants him to die.
• Have him intentionally, rather than accidentally, use the church bell to rid himself of the symbiote about 60% of the way through the film.
• Develop Venom as a proper character, show him thwarting Spider-Man and stealing his thunder. Show him using his knowledge of MJ to egg Parker on.
• Use Goblin as a more natural partner (your enemy is my enemy) for Venom.
• Use a similar finish to the movie as the two villains attempt to rid the world of Spider-Man.
• Let Harry come to his own (non-random) reasons for a change of heart and saving Spider-Man.
• Harry dies.
• Venom is defeated, but not dead. Slinks off to live another day.
• The End.