Character mistake: When Audrey Hepburn confronts Carrie Grant by saying "Carson Dyle had no brother.", he would have definitely wondered how she came to know about this, and who is her hidden source of information. (01:16:00)
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?
Continuity mistake: In the bedroom, Cary Grant puts on his glasses to read a note. When Audrey Hepburn says "I love you, Adam", he turns around and doesn't have his glasses on anymore. Next shot, they're in his hands. (01:25:20 - 01:26:00)
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.
Suggested correction: While Cary Grant doesn't see 'Dyle' written on the floor, Cary Grant sees Audrey Hepburn after she's exited the room and while fleeing she yells out that 'Tex is dead and wrote Dyle on the floor and you're the murderer' (paraphrased). That's how Cary Grant can refer to it in the next scene.
Suggested correction: You must have seen an edited version of the film. Not only does Grant go back to the hotel, but Hepburn explicitly tells him that Tex is dead and he wrote Dyle on the carpet.
No, Hepburn believes Grant is the killer - she phones Matthau (who she still thinks is the embassy guy) to tell him what Tex wrote on the carpet. When she leaves the room, Grant is coming up the stairs as she descends in the lift and he chases after her. She wouldn't have needed to try to get away from him if she'd already told him this.
Check out of the specific dialog in the scene: "Reggie! The stamps! Where are they? Reggie! Wait!" "Why? So you can kill me, too? Tex is dead. He wrote Dyle on the carpet." "I'm not Dyle. You know that." "But Tex didn't know it. You're a murderer." If your version of the film is missing this exchange, you have an edited copy. Since the film is in public domain, that is possible.