What do you need to do in order to mention a product on a TV show without the company suing you?
You would need to have the company's permission in order to mention thier product
Nothing. There are no legal grounds to sue you in this situation.
Why would they sue? Companies PAY for the advertising.
You've got it backwards. Companies PAY TV shows to mention their products. It's called "product placement"- and it's good advertisement for the product.