I was watching a National Geographics documentary on Midway and Bob Ballard's search for the Yorktown when they mentioned that the footage was taken by John Ford of Stage Coach / mess of westerns fame. The footage shown was really amazing. This version doesn't look so hot but it gives you a sense of the conditions.
Oral History - Battle of Midway
Recollections of Commander John Ford, USNR, Oscar-winning Hollywood producer and Chief of the Field Photographic Branch of the Office of Strategic Services (OSS), concerning his experiences making combat motion pictures under battle conditions. His film of the Battle of Midway subsequently became a popular movie feature.
Adapted from Commander John Ford USNR interview in box 10 of World War II Interviews, Operational Archives Branch, Naval Historical Center.