During Pvt. Benjamin's visit to Paris when she first goes to Henri's house and he is getting ready to play soccer the next morning he only has on one red sock. When he slips on Max's pee he has on two socks and then in the next second he is once again wearing only one sock and still holding the other.
When Judy finishes cleaning the latrine with her toothbrush she walks out of the room barefoot and carrying her black high heeled shoes. In the next shot however, she is wearing red, knee-high rubber boots which subsequently disappear, leaving her barefoot again.
While she showers, the mirror isn't at the correct angle for Captain Lewis to see her reflection with the blue dye . Standing where she was, she would have only seen the reflection of an empty bathroom.
When Judy meets Col. Thornbush and his wife in the Jeep, she meets the "Thorndog," Scrapple in the back of the Jeep and shakes his paw. Later, after the Col. says "let's let this soldier get some chow, mother," he pulls away and Scrapple is nowhere to be seen.
When Judy is on the phone with the recruiter in the hotel room, a pack of cigarettes appears and disappears between shots.
When the girls are in the war games and capture the Red Team truck the Sgt throws the keys away. Army vehicles do not require keys to start. The ignition is hardwired to a start button on the dash.
EDIT: Every vehicle in the Army then required a key. If the vehicle did have a starter button (a switch on floor akin to the old headlight dimmer switches in cars) it would still be secured when parked by a chain welded to the floor and running up through the steering wheel and secured with a padlock. You can start it, but you can't steer it unless you have the key. Throwing away the key isn't a factual mistake.
The berets worn by the soldiers and army officers in the film show the typical folds of berets that clearly have never been worn. In real army life, this is how you recognize new recruits. Any beret which has been worn for more than a few months will stay in the shape pushed to one ear.
Turkish Army officer in NATO HQ is portrayed with a mustache. However, Turkish army personnel are forbidden to grow a mustache. They are obliged to shave everyday. Hence, a Turkish army officer with a mustache or facial hair is not possible.
Col. Clay Thornbush (Robert Webber) says that, during the Korean War, he took orders from Douglas MacArthur in 1952. He could not have done this, as MacArthur was relieved of command by President Truman on 10 April 1951.
One of the ribbons worn by Capt. Doreen Lewis is for the Woman's Army Corps Service Medal. The Women's Army Corps Service Medal was awarded for service in both the Women's Army Auxiliary Corps during the period 10 Jul 42 - 31 Aug 43 and the Women's Army Corps during the period 1 Sep 43 - 2 Sep 45, even tho the Woman's Army Corps was around until the 1970's.
In the montage, Judy bounces a quarter on her bed and is supposed to catch it (like Captain Lewis did earlier), but only pretends to catch it. You can see the reflection of the quarter as it almost hits the bed, just before they cut to the next clip.
After the "war games", the women are back at their barracks and had been dancing to "We Are Family" and Captain Lewis comes in to address them wearing an off-white Australian-style "bush hat." On it, an improper eagle device, that of an enlisted woman, was clearly shown. Those of an officer do not have the circular brass base but are the more impressive large-eagle emblem of an officer.
When Benjamin jumps out of the airplane, the static line to deploy her parachute is not hooked up.
After the "war games", the women are back at their barracks dancing to "We Are Family" there is a close-up of the tape player that is playing the music. The "play" button is pushed but there is no tape in the player.
Just after the fight scene when Judy says she is going home, she passes a very large girl. A girl that fat would not be allowed to join the Army.
When Sgt, Ross is calling out the names for Private Benjamin's team for the war games his lips aren't moving when he says "Sawyer".
In the scene after graduation at the bar, the jazz trumpet music heard is not synchronized with the way the trumpet player is fingering.
When the troops are in their morning routines, mountains similar to California are seen in he background, but the movie is set in Mississippi, where there are no mountains.
When the new recruits get off the bus to start basic training in Mississippi as Judy sleeps on the bus, there are mountains in the background. There are no mountain ranges in Mississippi.
After Judy has arranged her posting to Europe, there are aerial shots of Paris, including the Eiffel Tower. This is followed by a voice-over of Judy describing how lovely it is "here in Belgium". The next shot shows her posting location - S.H.A.P.E. headquarters, which actually is in Belgium - followed by another shot with the Eiffel Tower in the background. Why would she live in Paris if she works in Mons, 2.5 hour's drive away?
EDIT: The answer is that it's not an error in geography. It's an establishing shot/scene used to show that due to the transfer to SHAPE in Belgium, she's close enough to visit Henri in Paris - thus setting up the visit later in the movie.
In addition to the mountains in the background of "Biloxi"--as well as the hills--which don't exist there, anyone who has been in Biloxi for even the shortest amount of time knows that it's not Bi-LOCK-see, as everyone says in the film; it's pronounced bi-LUCK-see. The new recruits could have pronounced it like the former, as this is how most people pronounce it until they know better, but the officers would have corrected them soon enough.