Probably less than half of passengers make the effort to dress for dinner at the MDRs, but it's perfectly appropriate to do so. The dining rooms and serving teams feel formal enough for you to be wearing dressy clothes. In fact, I'd personally feel out of place at an MDR dinner in shorts & t-shirt, but plenty of other passengers don't feel than way.
There is one pirate night, one cruise casual night, and one "optional dress-up" night on the 3-night cruises. We do suits/cocktail dresses for optional dress-up night and were definitely among the most formally dressed in the MDR, so there is no need for tuxedos or gowns.
Like the MDRs did a while back, Palo has relaxed its dress code. Most people dress more nicely at Palo than at the MDRs, but as long as you don't show up in swimwear or obvious athletic gear, you'll probably be seated.
You will get your dining rotation when you get your key to the world card at embarkation.
