T-shirts and shorts are specifically mentioned as not being acceptable for any dinner seating. Blue jeans are generally allowable on the casual nights. On all casual nights, a collared shirt of some type and long pants are the expectation.
For formal nights you will at least need slacks, shirt, tie, and a sport coat. Two formal nights on a 7-day cruise. One formal night on cruises of lesser duration. But fear not, because if you want to stick to a t-shirt and dungarees you can always go to the buffet for dinner. They serve an evening meal in the buffet which is really pretty decent, and normally has many of the items that are on the main dining room menu.