Storing cut button mushrooms vs whole button mushrooms
Anything will spoil more quickly if cut than if whole. It's all a matter of surface area.

The bacteria/fungi/mold/whatever can only attack the surface that is open to the air. When you cut the mushrooms, you open more surface up to attack, and hence they will be affected  more quickly. This is equally true for dehydration and loss of flavour (by evaporation), which are also linked to surface area.

With regards to spoiled mushrooms, a quick sinff will usually give away any dodgy mushrooms. They tend to stink like nobody's business when they've gone south. If they look right and smell right, they're most probably fine.