If you want to keep with a pure "shoot dumb zombies in masses"
idea, and dont want to go into a tactical (Battlefield) or
adventure (halflife) type of gameplay, you could include the following:

-add a level/mission goal to the game, that bases on
the speed that you kill the zombies, and
the "pickups" that they drop

similar to a classical spaceshooter, where the enemies
are also quite dumb.

In one level for example its the goal to kill zobies for
points, in a limited time. When you do that, you get a
"time extend"

In another level make a "zombierush" spawning masses of zombies comeing from doors,
the goel is to survive as long as possible.

In another level, make the levelpath quite linear,
the goal is just to reach the end-door in the quickest time possible,
the zombies drop powerups and give points.

In another level, make the player move on a fixed path,
(like a train). the player can just turn and shoot.

(p.s. a flamethrower would be nice too)