Get a program called Drive Snapshot and use it to create a snapshot image of your hard drive:
Drive Snapshot
http://www.drivesnapshot.de/
When encountering read errors on the source disk, Drive Snapshot will handle it intelligently and the result for you should eventually be that you'll get your video file with a blank spot where the read error occurred on disk.
I use this program to recover data for users. If the file system is NTFS or FAT32, then the default option is to only copy data that's allocated (although you also get the option to copy all sectors, you don't need this option in your case). If the file system is something that Drive Snapshot doesn't recognize, then it will just copy all sectors for you.
You can use that image later to write onto a new (replacement) hard disk. If the new disk is larger, Drive Snapshot will provide you with an option to increase the size of the partition to fill the new disk as well (but only for FAT32 and NTFS partitions).
Alternatively, you'll be able to mount the image directly as a virtual drive letter and the simply copy your file directly from there.