Stupid plot hole (kitty litter)
Kitty litter is not radioactive.
http://www.snopes.com/critters/gnus/litter.asp
There was a case of used kitty litter being radioactive, but that was due to the kitty in question receiving a radioactive dose from the vet. The litter itself was not radioactive.
Kitty litter can be used to soak up nuclear waste (just don't get the organic kind):
http://www.npr.org/sections/thetwo-way/2014/05/23/315279895/organic-kitty-litter-chief-suspect-in-nuclear-waste-accident
But again, this does not mean the litter itself is radioactive.
Another issue, although that isn't a plot hole because it can be explained by character ignorance, is that a Geiger counter cannot confirm the presence of uranium ore. Many things can cause elevated background radiation. For example, the radioactivity in the used kitty litter in the above story was due to I-131, a very different element.