Besides the usual ideas like hiring writers like Drew Goddard or even J Michael Straczynski and confirming more of a Spidey presence:

-Drop the sanitized Nerd Peter and make him a wiseass like the comics. As much as people harp on TASM being a poor adaption, it absolutely nailed Peter's personality. Plus him being a bit of an ass does lend more credence to Norman Osborn basically being what Peter would be without knowing responsibility.

-Actually make his side characters characters. Give Jonah some depth, make Flash more than just a bully, and actually do Mary Jane Watson right for once.

-Make the Spider-Man equivalent of Bat-Family with Ben Reilly, Cindy Moon, Mattie Franklin, and others.

-DO NOT END WITH DEATH OF SPIDER-MAN. It's just such a lame ending.