Dave mentions "Tupperware" in jest. Like radiation, plastic can take hundreds, even thousands of years to decompose.
The Care Bear sweatshirt worn by "Kate" includes the image of a rainbow. This is a sly nod to the strange colors in the sky as observed by witnesses of the Chernobyl disaster. These "lights" were ionized particles being emitted from the the destroyed radioactive core.
The ghosts in this film are not radioactive specters. They are a combination of dedicated "ghoul" performers as well as computer generated imagery produced using Intel Pentium II processors.
One of the wayward travelers injures his foot while lost in the abandoned city of Pripyat. This was intended as a reference to the large mass of radioactive materials beneath the decimated Chernobyl power plant. This mass is commonly referred to as "The Elephant's Foot."