While it made for interesting stories during the run of the show, romantic and sexual liaisons between passengers and crew members were (and still are) forbidden aboard cruise ships for a host of reasons.
While the long---establishing---shot shows the boat in motion, when they cut to the pool area, the sky can be seen above and it never changes. Equally, the water of the swimming pool isn't moving, nor is the people's hair blown by the wind. Not only that, when inside the cabins or the dining hall, there is no motion, no chandeliers swinging, no lamp shades swaying, nobody losing their footage, nothing to ever show they're on a perpetually moving craft. This reveals it's all filmed in a studio.