Wow, I'm always impressed to see claymation!
For backgrounds, you should consider using a green screen and adding an image, and then blurring it. It will not only speed up the process but will also make things look more crisp and give focus to your main actors. Also, the mushroom cloud scene doesn't fit well with the style of animation (which can be distracting).
Overall though, I'm impressed with how well you recreated Fallout. Even the radioactive goo!