In one shot of Charlie's hotel room door, the exterior of the door is white, in another the exterior of the door is wood grain.
The uniform of the American General Hallerton is incorrect. He is wearing a black tie (phased out in favor of the 'pink' tie and shirt in 1942); also his shoulder sleeve insignia denoting European Theater is sewn on upside down.
One of the admirals says "it has to be a neap tide so we can unload... with a minimum of open beach to cross... D-Day has to be June 5th or 6th... won't repeat these tidal conditions for half a year, at least with a moon". Apparently the script writers did not understand the meaning of "neap" (low tide), because they describe a spring tide (which has the most extreme high and low water marks) in terms of beach conditions but call it a neap tide (which has the least difference between high and low water marks). The reason given is historically incorrect as well, as avoiding defensive obstacles placed by the Germans was the main reason. (See the Wikipedia article "Normandy landings".) Also, the tide cycle is linked to the moon, so the next full moon would have been accompanied by another spring (high) tide, no half-year wait needed.
Garner is seen going ashore on D-Day on an LCVP that is marked for AP-215. The AP 215 is the Attack Transport USS Navarro. The Navarro was laid down until 27 June 1944. She was launched 3 October 1944, and commissioned on 15 November 1944. The Navarro took part in the Invasion of Okinawa, but was not involved in D-Day. It hadn't even been built yet. The Nevarro continue to serve during the Korean War and even transported troops in the early stages of the US involvement in Vietnam. She was placed in the Fleet Reserve in 1970, and scrapped in 1982.
When the Admirals were drinking heavily in the hotel room they reflected on their days at Annapolis when they were called "Naval Cadets" instead of "Midshipmen." Annapolis students were called "Naval Cadets" from 1888 to 1902 when these senior officers were likely enrolled.
Lt. Cdr. Madison was addressed as "Commander" throughout. This is incorrect. Naval officers of this and lower ranks are addressed as "Mister." Madison would have been "Mister Madison" to admirals, "Mister Madison, sir" to anyone he outranked.
The women's hairstyles, dress fashions, makeup and shoes are all strictly 1964 not 1944.
The C-54 airplane in which the Admiral and his staff travel bears a post-1948 national insignia (i.e., red stripe on the white bars) while the film is set in 1944. (Original post makes reference to a "USAF roundel" before before the USAF existed. The change applied to all US military aircraft and was coincidental and unrelated to the Air Force splitting off from the Army.)
When Julie Andrews is driving James Garner through the streets of London, the back projected image contains modern vehicles, including a Bedford TK truck, introduced in 1959.
William Windom is incorrectly credited as Capt. Harry Spaulding, but he wears the insignia of a Lt. Cmdr.