When Ellen is in the hotel room with Nick, her wig changes in mid-scene.
When Nick is watching Adam perform on the trampoline, the couple in the corner directly behind him get up and leave their table three different times.
When Nicholas is chasing Ellen in the car after leaving the hotel, they speed through a car dealership. Cars flee the building to allow Ellen to pass through without accident. Once Ellen's gone, the cars back into the store only to drive out again to allow Nick's pursuing taxi safe passage. The scene is spliced together rather than done in one shot, as evidenced by a green car parked streetside in the background that disappears before the taxi drives through.
When Ellen wants to phone the house, the operator gives her the number. Later, Bianca gives her psychiatrist a different number.
When Grace faints, Ellen takes some roses out of a vase to sprinkle water on her. When it doesn't work, she sets the flowers down on a chair. Later she goes to make a phone call, and sits in the chair, and the flowers appear on the table instead.
When the judge is reading his court briefs, it looks very much like pages of a script instead.
When Ellen rips the towel off of Bianca, to whom she is giving a massage, the towel moves a little too high and whatever Bianca is wearing underneath is partly visible.
Nick asks the judge to turn from page 4 to 7 in the brief. When the judge says "Here it is: page 7," he has turned over only two (one-sided) pages and would actually be on 6. (And just before he does this, the number of already-overturned pages differs from one camera angle to the other.)
When Ellen gets off the sub at the start of the film, she is wearing dungarees clearly designed for a woman. BUT as it is 1963 the Navy would NOT have women's fatigues in a submarine's stores. So Doris Day should have toughed it and worn men's clothes that was just too big for her! That's what would have been right in reality. But then, of course, they would NOT have shown off all of Doris Day's feminine curves.
Since Ellen was on a South Pacific island for five years; she should have a darker tan.
When Ellen is in the car wash, she pushes some buttons. It is obvious that the audio is unsynchronized.
A USN sub rescuing people from an island would have radioed their data home, thus ruining the surprise element necessary to the plot. The 1940 Portuguese tramp steamer (My Favorite Wife (1940)) works much better.
With Nick as passenger, Ellen drives his car to a particular hotel. Being a lawyer and knowing Ellen has been away from civilization for five years with no time to renew her driver's license, Nick should full-well know he's liable for allowing her, an unlicensed driver, behind the wheel of his car and, therefore, not allow it (especially as he wants to guarantee getting her to the right hotel to "accidentally" run into Stephen Burkett).
Strangely, despite their belief that Ellen has drowned, no one in the Arden household is at all concerned about leaving two very young children unattended in a swimming pool.
In the beginning, Grace offers to get Ellen a drink. Ellen quips, "You know very well, I don't drink". Later, poolside just before Steve appears, Nick asks Ellen if she would like a scotch. After three years of marriage, Nick should know Ellen doesn't drink.
Nicholas Arden, a lawyer, in the climactic court room scene initially addresses the judge as "Yes sir" instead of "Your Honor", although he does gets it right later. An experienced lawyer would know better.
(at around 1h 35 mins) When Stephen Burkett is called before the court, Judge Bryson says, "What's your story, Tarzan?" Having not met the man nor heard his and Ellen's story on the island, there would be no reason he should have called him "Tarzan".