Physicist Kip Thorne consulted on the movie. The physics are accurate.
Miller’s planet (the ocean world) was spinning extremely rapidly and it was located just above the event horizon of the supermassive black hole, Gargantua. The rapid spin of the planet provides a slingshot effect when you take off in the direction of the spin. This is true on earth as well, and is most pronounced near the equator, but the extreme spin of Miller’s planet makes it much easier to achieve orbit.
The proximity of the black hole is the cause of the extreme tidal forces which create the tidal waves on the planet, but would also help them take off for the same reason (tidal forces affect all masses moving in the gravitational field).
The lack of spaghettification is a known and established fact with supermassive black holes. What you were expecting is what happens with stellar black holes (10x mass of the sun to 100x), not with supermassive black holes (millions to billions of times the mass of the sun) whose event horizons are much larger and therefore have less extreme gravitational gradients (the source of spaghettification).