Leave the mistake in and then correct it.
I think leaving the mistake and correcting later is very confusing and possibly discouraging to students. What is your response to that?
In the same video, note your mistake and correct it.
I don't see why you would want to leave the mistakes in there. Someone might not grasp the correction!
I just remember getting incredibly frustrated after basically learning the wrong thing in the first video and then having it corrected in the second.
Maybe youtube isn't the best medium for his videos and he should instead find an option that allows and easily facilitates future edits.