Dear Mr. Allan,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Logbooks of U.S. Navy Ships and Stations, 1941 - 1983 in the Records of the Bureau of Naval Personnel (Record Group 24) that include the deck log of the USS Mount Vernon (AP-22) from 16 June 1941 through 17 January 1946. For access to and/or copies of this log, please contact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
We also located World War II War Diaries, Other Operational Records and Histories, ca. 1/1/1942 - ca. 6/1/1946 in the Records of the Office of the Chief of Naval Operations (Record Group 38) contains war diaries and reports concerning the USS Mount Vernon’s activities during World War II. These records have been digitized and can be viewed online through the Catalog. Please keep in mind that the Catalog does not always list files in chronological order.
We also searched the Catalog for photographs of the USS Mount Vernon and located a photograph of Soldiers of 91st Infantry Division Debarking the USS Mount Vernon in the Records of the Office of the Chief of Transportation (Record Group 336) that has been digitized and can be viewed online through the Catalog. There may be additional photographs of the USS Mount Vernon that have not yet been digitized and uploaded to the Catalog. Please contact the National Archives at College Park - Still Picture (RDSS) via email at firstname.lastname@example.org to request a search for additional photographs.
Plus, we searched online and located photographs and other information about the USS Mount Vernon on the unofficial website NavSource Online. One source on this website that is particularly worth noting is the AP-22 Mount Vernon Cruise Book 1941 to 1946, which is a series of 10 web pages with text and photographs taken from the cruise book. US Navy cruise books are unofficial publications published by a ship's crew to document a cruise, deployment, or in this case an entire war and its immediate aftermath.
We hope this information is helpful. Best of luck with your family research!