If he has official records charging him with the theft of non-matching baby shoes, and he has an otherwise typical white collar resume, he might actually be able to explain that one away. Unfortunately all of the real criminals have explanations for how they were wrongly convicted too.

Whether it's a big problem depends on whether he has to check the box on the job app... it's easier and cheaper for HR to interview applicants with clean records, that way they don't have to incur the time, expense, and risk of adjudicating the circumstances of such a record.

He should look at the online applications of many airlines, regionals and majors, to see exactly what they ask. He should obtain a copy of his FBI database records (I think you need FOIA, but that's easy).