I used to ride no hands a lot. I mean the handlebars were there to hold the brakes, or something to pull on for really steep hills - that kind of thing.

You can tell a lot by riding no hands, but it is much simpler and quicker to learn to use a piece of string and how to examine a bike than learning what your bike is doing no handed. Bent frames tend to lean, because you need to shift your position to compensate. Loose or stiff fork bearings should be felt before getting on the bike, as well as wheel alignment in the forks and stays. My folders are *****y no handed as their forks are relatively straight, and will snap to the side with little warning unless the surface is really smooth.