When the rescue aircraft spots the survivors floating in the ocean, during different flyovers the number of survivors and their groupings vary.
One military dude tells another that there are more than 300 reported survivors floating in the ocean. In no scene prior to this, are there nearly so many survivors pictured.
When the Indianapolis is attacked relatively early in the film, Lt. Cdr. Hashimoto preserves the Kaiten, much to their pilots' chagrin, and then FOUR torpedoes are seen having been fired. However, during the court martial of Charles B. McVay III, he testifies as to having " . . . fired only three torpedoes . . . ".
After the Indianapolis delivers the atomic bomb to Tinian, there is a shot of a B-29 with "Enola Gay" painted on its nose. This was the airplane that dropped the bomb on Hiroshima. In reality, the name was not painted on this aircraft until the day before the mission.
The Japanese submarine's spotter would not state the USS Indianapolis' speed as "approximately." He would state the exact speed.
When the torpedoes from the Japanese sub strike the USS Indianapolis, within a minute fires are all over the decks of the target ship. The torpedoes would have struck at or below sea level, and the ship's decks would not be on fire so soon.
The seaman on the USS Indianapolis is clearly not writing anything on his letter pad when he is writing to Ellie, prior to being torpedoed. There is no ink on his notepad.
The US army uniforms (in the Philippines, end elsewhere) have only stars on the lapels, no other insignia.
Around the 49th minute, one can see green water under the men floating in the ocean. When water appears this colour, it is not remotely deep.
In the scene where a seaplane lands at sea to rescue the crew, the plane used is a Grumman Albatross. However, this aircraft was not put into service until 1949. The real life aircraft that rescued the crew, was a Catalina PBY.
In the poster advertising the movie, the American Flag has fifty stars, as it does now, but that flag was not adopted until Monday, July 4, 1960. The flag that should have been shown, which those men on the Indianapolis served under, was the forty eight-star Stars and Stripes, which was valid from Thursday July 4, 1912 to Friday July 3, 1959, and is even seen hanging high in Grand Central Station in Hitchcock's North by Northwest.