My A string has fret buzz when it's open, but otherwise there's no fret buzz. Also, when it's slapped, it seems to go out of tune fast (though that's probably due to something I'm doing wrong).

How do I fix this?
might need a new nut. is it a fresh string? sometimes strings need to get broken in so the problem might just go away. I'd say if it doesn't go away, take it to a tech at a local shop and have him give it a once over. There might just be one little thing out of place that only a trained eye can see.
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i have the exact same problem! its VERY frustrating. i never thought that it may be the nut....
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Usually when the string is only buzzing when played open, its the nut. The slot is cut too deep, and the string is buzzing against the first fret.