you can also use a live CD distribution of linux to try to copy files in USB stick and see if they are corrupt. If no, then the problem must be in the Operating system
Did the corruption occur in a single disk. If so, then try a different drive and see if it gets corrupt too. If it doesn't get corrupt, then the problem is in your USB drive.
you can Use a voltmeter to check if the supply voltage of the USB port is 5V. If it is not constant 5V, then PSU might be a problem.
What sort of hardware are you driving with the PSU? If you have a dual core processor, most likely, the PSU is over exhausted. Then you might consider replacing it. If possible, try to open up an extra RAM, excess harddrives and optical drives, and just connect the USB to see if data corruption persists. If no, then your PSU was overloaded.