The lion's head entrance to the MGM Grand featured in the movie has since been removed because many Chinese gamblers avoided the casino (or entered through the back entrance), due to the feng shui belief that entering the mouth of the lion was bad luck.
When Roper is watching the soap opera, and throws the ring away to watch his entourage chase it, it clearly falls out of the box as it skips on the floor. Yet, when Rollo puts it on, before Roper takes it, he takes it out of the box.