I actually read the novel, and the movie is much more faithful to it than most screen adoptions. I agree that the model work was quite poor, but extremely forgivable given the strong story-line and acting. It captures the feel of the naval war in the Pacific for the Americans quite well. Since quite a number of other reviewers have agreed with me, the rest of this review will concentrate on differences between the movie and what actually happened.
Motor torpedo boats did sink a battleship once--in World War I. The PT boats of this war never sank anything larger than a destroyer, and few of those. Many had their torpedoes removed to fit small cannons, useful for sinking barges and floating drums. While new craft could reach 40 knots in calm water, engines tended to wear out quickly, and in combat conditions, the PT boats were generally slower than the ships they were trying to attack.
There never was a daylight battle between any Japanese battleships and American cruisers. There were two night battles, one at Guadalcanal and one at Surigao Strait in the Philippines, and in the latter, the American cruisers were backed by six battleships, versus only two Japanese battleships and one cruiser.
The mighty Yamato never fought anything more formidable than destroyers, and doesn't seem to have scored a single hit on an enemy vessel. Her sister Musashi never sighted an enemy vessel. Both were sunk by aircraft. Their poor performance might be explained by their spending most of the war at anchor. They were comfortable ships even for enlisted men, at least by the standards of the Japanese navy of the time. Yamato was often called "the Yamato Hotel" and the Musashi "the Palace."
The U.S. Navy did very little mining during World War II. Laying mines to protect Guadalcanal would have been a wonderful idea, but then, as now, mines were unpopular weapons with the admirals.
The final battle in the movie and the novel seems to be most similar to a night battle on November 13, 1942 between a US force of cruisers and destroyers and a Japanese task force built around two older battleships (each about half the size of Yamato). The US force suffered heavy casualties and two US Admirals were killed, but it crippled one of the battleships, leaving it vulnerable to US bombers the next day.
