bad u-joints make noises. Clunking when you put the car in gear, rattling at higher speeds.
They make a LOT of noise before they fail. It's not a subtle thing.
I would think you could block the car in place, put it in park, jack up the rear, and try rotating the driveshaft. A bad u-joint would be sloppy.
I've never tried anything like that. I've just driven the car until the noise is too annoying, then taken it to a shop to check it/fix it.