To add to VOiDs response about movement, try adding a constant force while movement inputs are being pressed and applying some linear drag when no movement inputs are being pressed or when a change in direction happens. Should result in "tighter" controls. Overall very well done.
Some more challenges you could tackle:
Adding some sort of dust particle when changing direction
Adding a reload system; Make the character slower when he is in a reloading state.
Health Bar for player
Blood particles that overlay on the ground and stay for some permanence
Have zombies "know of each other" so they don't stack up and avoid each other. This would result in a horde-looking effect.
All in all, the game is very nice and you still have 30 days!!