Even when it becomes clear early on that the characters and conflicts on the "reality" show are staged, it never occurs to the CSI team to interview the people behind the scenes, not even the mysterious "producers" that the suspects constantly refer to.
The CSI's arrest Shae based on the fact that they find traces of her fake tanning spray on the ice sculpture, that she apparently left when she broke off an icicle to kill the victim. But in a flashback, Shae is shown spraying herself with the tanning solution right next to the sculpture. Thus, she could have easily explained why her spray was on the sculpture.
Natalia professes not to know why the Statue of Liberty is green. Her character, an expert in chemistry, could not possibly be unaware what color copper turns when it oxidizes.