1_ Change the controls from left and right arrows to up and down. The players doesn't see the zombies going right and left right away, they see if they are up or down and then think which is the equivalent: this is a very fast rhythm game, the player doesn't have the time to figure out which button should be pressed. Also on that note, add control configuration in the menu if possible. Yes, it is extra work, but it's better then get negative reviews because some people found the original controls akward (I know that's my only gripe with Super Meat Boy).
2_ The input of the player actually disrupts the music instead of building it, like most rhythm games: the actual input of the player is a gun blast that doesn't fit the music and the actual drum is already in the song playing. The coolest part about this kinda of game is that when you do it perfectly, you get to hear the music as it was intended. I'd suggest a change of music style to either punk rock or heavy metal, and instead of a drum, the player instrument would be a gun(here's an example).
3_ The indication of when you should press buttons should be where the player is watching the game, instead of a separated hud. In Guitar Hero they had the luxury to do that because the information on the other part of the screen is negligible. If you'll follow the rock-with-guns suggestion of the second item, bullets being grabbed on the road could be cool; or, if you want something simpler, yellow lines in the road, with the markers on the car.
4-I feel like something more interesting could happen in the end of the level. What about this: if there's no zombies, the group gets to a crowd that hails them as gods, groupies get in their car with booze and they peace out to the next level. If there's still zombies, they attack the crowd and the band shrugs and leaves as everybody is running for their lives.