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Surgeon and civil engineer come to mind as rofessions where you can be criminally incompetent.

Again, surgeons and engineers have to take certifications to prove they have the credentials they speak of.

They would have to forge documents on top of lying on their resumes.

You're really drifting from lying to fraud.

People can have certificates and be incompetent, and lie to get a job. See http://www.texasobserver.org/anatomy-tragedy/ (discussion: https://news.ycombinator.com/item?id=6306289) for an example of a surgeon who lied about the cause of medical complications.