If you want to pursue it, yes, get the FAA CD. It will show previous registered owners, liens, any form 337's filed, and other information that you may find useful. For only us$10, it's good insurance.
Check the engine logs for "yellow tags", the FAA form 8100's that come with new and reconditioned parts. These aren't required to be included, as just a sign-off will suffice, but most mechanics will leave them in the logs, or include them in other aircraft records. The more detailed the records, the more confident you can be, but anything "missing" can be missing for a reason.
If all you find is a rubber stamped sign-off, it doesn't mean there are problems, but you can't eliminate them, either.
Complete logs since new is a plus, but complete logs since overhaul are mandatory. There should be some way to verify total times and events, and of course, any serial numbers listed must match what's installed in the plane.
