First of all, Nathan should have died at the end of Season 1 like it was shown. His character arc had already been established in that he started off as an opportunistic politician who made a heroic sacrifice to save New York, and his survival cheapened that. Not to mention it would have provided Peter with some guilt in that he survived while his brother did not.
Speaking of Peter, he also should have lost all the powers he gained after he exploded. After all, just as he absorbed powers like a sponge, he should have been able to wring out those powers like a sponge. This would force him to only absorb a power at a time just like he's doing in the fourth volume out of fear that, if he absorbs to many powers, he could overload himself again and lose control.
The family of Nikki, DL, and Micah should have essentially been written out of the series after Season 1 as well, as their story was also pretty much over and done with. Proof of this of course, is that Ali Larter's character of Nikki once again was forced into another personality and ends up dying anyway, and now plays a totally new character who is currently being wasted.
Hiro, I think, should have stayed in the past, and it should have been quickly established that HE, not Adam Monroe, was the Kensei of legend. He had already undergone the "hero's journey" in season 1 and the last two seasons have been desperate attempts at trying to recreate this. Maybe Masi Oki could have made a few guest appearances from time to time, but that would be it. Or better yet, hold off on that and have Hiro's go back to when the Company was formed and put together. That way, we not only get to see who these people are and what their actual powers were, but how characters like Hiro's dad, Angela, Maury, Arthur, Linderman, and others became the way they did.
As for the new characters, West clearly should not have been there, or at least have been masively retooled, as Claire's relationship with him was just utter fail and a retread of her not trusting her adoptive father in season 1. Same goes for Maya and Alejandro. And Matt Parkman's dad should have been the big bad seeking revenge against the Company in the second volume that should have been the enemy of the company and the heroes, not Adam. That way, you could have easily told the backstory of the Company and made an frightening and legitamate threat at the same time.
Likewise, Sylar should have stayed away for much longer, still kept as a prisoner by the Company to be used as a weapon of last resort by them, that the situation with the Nightmare Man becomes so desperate, they have to use Sylar in order to stop him, much to the objections of Noah, Peter, and the like.
Also, I think Suresh, Matt, and Molly should have gone out and looked for more Heroes. This way we could have been introduced to the new characters and thus promote the original idea of the cast being rotated or gradually phased out, while maintaining the premise that there are ordinary people with extraordinary powers.
Another big problem was the four month gap in-between volume 1 and 2, in which lingering plot elements from volume 1 were not adequately followed up on and eventually left to just wither away, e.g. as the Matt's troubled marriage and the expected baby. Why not tie THAT into Matt's dad in an attempt to have a second chance to be a proper grandfather that he failed with Matt as a father?
Of course, where things really went wrong is that Heroes was repeating the very plot elements from the first season: a huge threat that required the heroes to save the world, paintings depicting the future, time travel to a dystopian future, Claire not trusting her father, Peter and Nathan not trusting their mother, Sylar trying to acquire more powers, etc. It gave the sense that Heroes was just standing still instead of expanding it's premise and developing it's characters.
Then there was the real jump the shark moment (one of several apparently) in which the show decided to steal the plot device from the 4400 and make it so that normal people could potentially have powers. Thus the two normal characters who acted viewpoints from the audience perspective, Mohindir and Ando, became just two more superpowered people and lost their role in the series.
Basically, the show should have done what caught people's interest and made it fascinating in the first place--concentrate on character development and maintain a sense of realism rather than imitate comic books instead of be inspired by them.