cyclic redundancy checks are usually hard drive sector error related, but not always. They can also sometimes occur on a bad dvd, a scratched DVD, a DVD drive that is having issues, or a hard drive with significant fragmentation.
I'd try first running disk defragmenter, and next download and run speedfan to check your hard drive for any SMART code errors.
If you have an older hard drive, since new SATA drives are fairly cheap and hard drives have an effective 5 year lifespan on average, you may want to think about grabbing a new drive.
Edit: apperently the FFXIV disk uses some odd copy protection that is causing some issues with some DVD readers. you may want to check for a firmware update for your DVD drive, or if it is an older one, swap it out for a newer faster one for around $20 for a 22x DVD RW from newegg. A few people are also reporting physically damaged disks, scratches or other write damage. looking at the bottom of the disk, you will see a discolored small round spot about the size of a large pin head in the disk if you have one of the defective disks. I've only seen one report of that though.
Edited, Sep 22nd 2010 8:50pm by Kaolian