I heard that ozone degrades plastic. Is this going to cause everything plastic in my room to be worthless after using the BIG BLUE?

It’s true that ozone can degrade materials such as plastic. However, under normal use the concentration produced by the BIG BLUE and the short contact time is not nearly enough to cause any kind of problems. It takes a tremendous amount of ozone to cause this type of damage, and the contact time would have to be months/years, not hours/days.