Revealing mistake: When McKay and Ramon are riding into Blanco Canyon to rescue Julie, you can see a diesel loading shovel with its bucket raised in the bottom of the frame of one of the scenic shots. Presumably the scene was shot in a quarry and they didn't get all the equipment out.
Other mistake: In the opening scene on the airplane, one of the men tells Lt. Cable, "The captain wants to know if you'd like to sit up in the cockpit with him?" Buzz Adams, the "captain" referenced in this line, is only a lieutenant. Admittedly, "captain" is a standard aviation term for the pilot of an aircraft, but it would be unlikely to be used in this situation, since the term has a specific military meaning.
Continuity mistake: Near the end, when Scotty is driving Judy to the Mission, the view from inside the car of the road shows that Scotty is driving on the left-hand side when he should legally be on the right. It is not a one-way road, and it appears that the shot was flipped.
Visible crew/equipment: When Isabel Jeans is telephoned by Madame Alvarez and told that Gigi has refused Gaston's advances, she gets out of bed and walks across the bedroom. As she passes a cheval (full length) mirror a pair of retreating jean-clad legs and a hand feeding out cable can be seen in the reflection.
Continuity mistake: When Major Pollock sits down at his table in the dining room, he takes the napkin's ring off and after it falls he places the ring on the table and the napkin on his lap, but when John says, "Good morning," the Major's napkin is rolled in its ring and back on the table, then it's gone again. (01:35:00)
Revealing mistake: In the opening credits, Richard Widmark is driving a car with Doris Day in the passenger seat. Widmark does not turn the steering wheel, even though the rear-screen projection shows him going around a curve.
Continuity mistake: Lucy storms out of Michael's car; the car has the hood (almost) entirely in direct sunlight, but when he opens the door to give chase to her it's mostly covered in foliage shadow. (00:06:40)