At one time, homosexuals were referred to as "Nature's mistakes." There's a line in the classic horror film, "The Haunting" (1963), that uses this term to refer to such a person, unless it has been edited out.
I think the appropriateness of the term "mistake" as applied to us depends on the context as well as point of view. When people call us "unnatural" or criticize our use of medical science to try to ameliorate our sense of discontinuity, I frequently use the example of a cleft palate. Any congenital deformity will do, but this one is sufficiently common and well-known to make it particularly useful.
We don't believe that children afflicted with this condition are "mistakes," but I'm sure most of us believe that the condition itself is. It seems fairly obvious that having a cleft palate is not what Nature intended; it is counterproductive, from the point of view of personal survival and survival of the species. Similarly, it seems clear to me that having one's gender and sexuality align with one's physical sex is what Nature intended, simply because that's how our species survives.
Of course, they don't always; we're living proof. That doesn't mean we ourselves are mistakes, anymore than is the child afflicted with a cleft palate; but, speaking personally, I would much rather have a body that fully complements my womanhood than the one I do have. Such a body is designed to complement certain natural inclinations, whereas the one I currently have does not.