Like any other major city, prostitution is a thriving industry in Las Vegas, though it's not legal within the city or the surrounding Clark County. However, as you suggest with your quotes around "services," the leafleteers (also known as "slappers") on the Las Vegas Strip aren’t explicitly advertising prostitution, only implicitly.
Yes, the flyers graphically depict women selling their services, and yes, everyone knows that those services in Sin City are sexual. Still, since the leaflets -- and booklets in the ubiquitous newspaper dispensers -- advertise only personal "entertainers" and "escorts", according to the letter of the First Amendment to the U.S. Constitution, that’s legal.
Couched as adult entertainment, these leaflets are ostensibly selling nothing more than what’s sold in gentleman’s clubs all over the world. It’s the same service, again ostensibly, only in the comfort of a hotel room. And if that service happens to cross a particular line into illegal territory, then the entertainer and her audience risk suffering the consequences.
