Really awesome! I love all the little details, like the uranium sticks for light but being the reason that you only have 30s per zombie. Just enough of a challenge and a really enjoyable experience.
Without downloading and looking at the source and project in unity, I'm wondering if the jumping bug has to do with the ground collision detection. There's a slight bounce in the walk, and I'm wondering if while bouncing during the walk, your colliders lose contact with the ground and so the game thinks you're in the air as if you already jumped and so you can't jump again.