In "The Tip of the Zoidberg" we see a fairly well adjusted Zoidberg get his head crushed by the Yeti. Was the Yeti injury the cause of his incompetence?
I don't think Zoidberg is incompetent. Zoidberg is actually a competent physician, but not for humans. He is competent in the anatomy of aliens, and even Mom recognizes his skillfulness with aliens. In "The Tip of the Zoidberg", Mom sends Zoidberg to help kill a Tritonian yeti for her bio-weapon. And it was also Zoidberg that figured out that the Professor had yetiism and not hypermalaria, and knew how to cure him.