Continuity mistake: When the French inspector is interrogating Audrey Hepburn, he asks "Why did he want to leave France?". The shot changes to the back of the inspector and Audrey replies, "Leave? No." Then the inspector makes a rough movement with his body and head to his right, but the movement is brusquely cut and replaced by a front shot where he is sitting perfectly still, as he was doing in similar previous front shots.
Visible crew/equipment: As Reggie and Sylvie are walking around the indoor swimming pool, the boom arm and mic are reflected in the glass as they turn the corner.
Continuity mistake: Towards the end of the film, 'Adam' meets Reggie at the meeting where she is working as a translator. They hurriedly leave for the venue (gardens) where her late husband had his last appointment. She leaves her friend, Silvie (who has several appearances throughout the film) also working there as a translator. Yet no sooner have they arrived at the gardens than Reggie sees Silvie sitting on a bench reading a magazine, waiting for her son to return from the stamp market. How could she possibly have got there so quickly?
Plot hole: Reggie finds Tex's body stretched out on the bedroom floor, his feet tied to the radiator next to the wall and his hands bound to the bed frame, suffocated with a plastic bag over his head. The bed is a twin-sized, wood frame that Tex, a tall, strong young man, could have pulled the end of it with his hands and arms close enough to his face to at least attempt to tear a hole in the plastic bag so he could breath. He was obviously conscious early on because he wrote the name "Dyle" in the dusty floor with his finger. Considering the floor is covered in dust, there's not even the slightest sign of a struggle to free himself. Instead he just neatly prints the name on the floor before he dies.
Plot hole: When Walter Matthau is interviewing Audrey Hepburn in his "office," she is looking at a picture. She identifies various faces in the picture. Matthau correctly identifies the person without knowing which face she was asking about. Other than her husband, he could not know which of the other three faces she was studying.
Plot hole: When Cary Grant is chasing after Audrey Hepburn where she has to meet Walter Matthau outside the Paris Opera he shouts "Reggie stop - that man is Carson Dyle". Tex recognised him, that's why he wrote Dyle on the carpet. But Cary Grant hadn't gone back into the room at the hotel, so he couldn't even have known Tex was dead.