Continuity mistake: When the butler tells of Harry Lime's death, at the start of the conversation he can hardly speak English. As the conversation goes on, his English gets better and better, until at the end it's perfect with just an accent.
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Suggested correction: He is reluctant to speak English at the start possibly to avoid trouble but later decides otherwise.
Continuity mistake: Bill Kirby enters the bar. He asks Bob the waiter about his wife. There's a cut during this brief exchange, and the girl sitting at the table in the background changes position suddenly (she was browsing a magazine, now she is holding it still and fully open). (00:02:35)