First, check your Ram. With a separate (trusted) computer, download a copy of the ISO for Memtest86 and burn a CD from it. Boot your computer to that disc, and allow it to run for a few hours. Yes, a few hours. You want it to complete all the tests, more than once.
Why? You could have a bad stick of Ram which only produces errors when moving large files through it. I've seen it more than once. In one particular case a few years back, I myself had a machine with 3x1gb Ram in the box, one stick of which was bad. Windows installed fine with the Ram, and there were no operational issues. Only when I attempted to copy some large files did I develop this same exact issue... CRC errors. One Memtest86 later and I was removing the bad stick.
Could it also be a bad drive? Sure. Run Chkdsk on it, if you are using Windows. With the drive connected, right click on the drive in Computer/My Computer, choose properties, the Tools tab, and run Error Checking. Make it do everything from that panel.