He wouldn't have gotten it inspected if he wasn't serious about buying it and if he didn't plan on purchasing it (provided it passed the inspection). Your wife probably either made it sound like a done deal to him, or didn't express the possibility that the deal wasn't yet rock solid until you got it all straightened out. So, unless she did express to him that the deal might fall through, it's at least as much, if not more, her fault than his.
Ask yourself, if you were in his shoes, and knew what he knew about the deal, if you would get the car inspected yourself. If the answer is "Yes", then make him whole again. If the answer is "No", just give him the deposit back. And if you're not exactly sure what he did and did not know about the status and true availability of the car, then just split the costs evenly.
EDIT: Your wife accepted a deposit check for the vehicle. That is "Intent to Sell", and the prospective buyer has every right to have the car inspected by an independent mechanic before completing the transaction. He was absolutely in no way wrong to have the car inspected; it's precisely what he should have done before completing the sale. Your only "out", legally, is if it was made very clear that you had to approve of the sale first, and that it wasn't made out to seem as if it wouldn't be a problem.
