No, they are used differently. 'Don't get me wrong' is essentially saying "Don't misunderstand what I am saying, or what I just said". "He gets into trouble sometimes, but don't get me wrong, he's still a good boy". 'Make no mistake' stresses the truth or fact of what you are about to say. "He gets into trouble sometimes, and make no mistake, he'll end up in prison if he's not careful."

They can be used as similar phrases, though I think that when you say “make no mistake” you might sound more serious than “don’t get me wrong.” They’re not exactly the same.