The only time nowadays that I see grammatically incorrect double negatives like "don't have none" are when writers deliberately break rules for effect. I can't remember the last time I saw anyone, published or not, write such a double negative while thinking it's grammatically okay.
So, that's not the kind of double negative I have qualms about. This next kind is. My example comes from Eating Las Vegas, 2012 ed. by John Curtas, Max Jacobson, and Al Mancini. This book talks about 50 "essential" restaurants in Las Vegas. Keep in mind that despite how this particular quote (from page 44) comes across, I'm taking it out of context. The reviewers admire this restaurant (named Bouchon).
Bouchon is a copy of a copy and has exactly the soul of one. That doesn't mean the food isn't fabulous, but it does mean...
Look at that second sentence. Why use two negatives to express something positive? Because the author, John Curtas in this case, is trying to make a point that even though this restaurant is a terrific French bistro, one aspect of it bothers him.
Had I been the editor, I'd have asked John if he really wanted to start out text that's supposed to be praising the restaurant with quite that much negativity. Also, I'd ask his opinion about whether the double negatives might make his thoughts harder to follow than they have to be.
I'd have suggested:
...and has exactly the soul of one. Yes, the food is fabulous, but...
Some might argue that the "Yes" in that revision is unnecessary, but I think putting it in captures the feel and intent of the original better than just saying "The food is fabulous, but..."
Sometimes using negatives in this way can enhance a text, but I'll save my favorite negative-to-express-positive example of all time for the next post. Hint: it's from The Hitchhiker's Guide to the Galaxy. Any guesses?