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.
Suggested correction: I believe Matthau/Dyle handed the pictures to Hepburn and knew the order in which he had put them, and therefore who was in each pic: first, second third.., as she went through them in order from the top.
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.