When Frank decides to buy Helen a gift to commemorate their
first and last date she picks a stature of Kwan Yin. The clerk says the Kwan Yin means "joyous symbol of fertility" (at 34:32 on the DVD). Kwan Yin actually means "Observing the Sounds of the World" and is primarily considered the Goddess of Mercy, Love and Compassion. Her fertility aspects are minor and would not be mentioned by a Chinese person.
As Frank and Helen are checking out their groceries at the commissary, the checked items are shown several times, and although the clerk appears to be moving them toward the person boxing the groceries, the items shown are the same in each shot. Also, any family with 18 children would buy milk in gallons, not in quarts (they purchase about 20 quarts).
In the Scene where Van Johnson meets the combined family for the first time, the kids wipe their hands on his uniform shirt, leaving raspberry jam and indelible ink stains. First is the raspberry, then the ink, but when we see the front of his shirt after the ink is applied, we can't see the jam. In the very next scene, the shirt is spotless.
When Lucille is holding baby in the hospital, it is wrapped in a blue blanket. She clearly asks the nurse "Could you hold HIM up to the window so they could see HIM? The baby is a BOY. However, in the closing scene when the oldest son leaves, the Baby is clearly wrapped in pink which in 1968 meant a girl.
Driving back from the Japanese restaurant, the trio are on the upper deck of the San Francisco Bay Bridge. The upper deck runs westbound, into San Francisco from the east. To return to Alameda, eastbound from San Francisco, one would drive on the lower deck. This was likely known by the filmmakers who used upper deck footage because it's much nicer than the tunnel-like experience of the lower deck.
When Frank goes to his carrier's flight deck to halt the launch of the mail plane, he is wearing a ship's ballcap. After packing, he returns to the flight deck wearing a combination cap. In fact, neither hat is permitted on the flight deck during flight operations, as they are easily sucked into a jet engine intake, causing foreign object damage. Further, no one is permitted on the flight deck without the cranial helmet, goggles, and hearing protection that we see the catapult launch officer wearing, except for pilots and necessary flight crew going to and from their aircraft.
When Frank learns that his wife is pregnant, he goes to the flight deck and convinces the catapult launch officer to stop the launch of the mail plane. In fact, the catapult officer does not have that authority. Unless there is a mechanical or safety problem, the Air Boss (who is never on the flight deck) is the lowest ranking person with the authority to cancel a launch.
At the urging of her daughters who are trying to make her look more glamorous, Helen reluctantly agrees to wear false eyelashes on a date - although the actress who is playing her (Lucille Ball) obviously is wearing false eyelashes throughout the entire film, including scenes that occur long before the one mentioned.
After the wedding the family moves in the new home. While the children are being assigned their rooms "Mike" is seen bringing suitcases upstairs. A couple of scenes later he is seen bringing the same suitcases upstairs a second time.
The goof item below may give away important plot points.
Helen learns she is pregnant on Christmas morning.
But seven months later (a fact established by July postmarks on several envelopes while her husband is away at sea at 93:24 on the DVD) she displays no physical signs that she is less than two months away from giving birth.