A mouse can enter a crawl space through any cracks or holes 1/4 wide, they will then start building nests, contaminating food, causing damage and potentially spreading disease.
Imagine the scene... there is heavy rain and your basement has begun - yet again - to fill with water. You have done all the right things with regard to your gutters being clear of any clogged debris and all downspouts are extended, but why is this not keeping the basement dry?