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I made a mistake with the time.

is this sentence correct?

thanks
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Sure.

"I know I told you the movie started at 3, but I made a mistake with the time. It's really 3:30."

But it may be more natural to say "I made a mistake ABOUT the time" or "I was mistaken about the time."
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Grammar Geek"I know I told you the movie started at 3, but I made a mistake with the time. It's really 3:30."
But it may be more natural to say "I made a mistake ABOUT the time" or "I was mistaken about the time.""I was mistaken about the time."
seems the most natural to me.

Also IMO:
I had the wrong time
might work.