We were on the Tahitian Princess in early May. There were two formal nights for the 10 day cruise. More than half the people were dressed formally; the rest were pretty dressy, but not tuxes and evening gowns. More wedding-type dresses.
For other nights, things are a bit more casual, with many women wearing either sun dresses or slacks. We never ate in the dining room other than dinnertime; the Panorama Buffet filled our needs and times better during the day; we loved eating lunch and breakfast on the deck behind the Panorama Buffet, watching the islands go by--or the wake on sea days.
If you have any other questions about the cruise, I'd be happy to reply. There are also many great threads on www.cruisecritic.com
about the Tahitian Princess, detailing many great shore excursions that last longer, do more, and cost a whole lot less than the Princess offerings. Great source of info.