xfsdump/zfs send are file system aware, unlike dd, and can detect fs corruption (ZFS especially having extensive checksums). In fact, any info cp sees about corruption comes from the FS code parsing the FS tree.
However, except on zfs/btrfs, data block corruption will pass unnoticed. And in my experience, when you have bad blocks, you have millions of them -- too many to manually fix. As this causes a read hang, it is usually better to dd copy the fs to a clean disk, set to replace bad blocks with zeros, then fsck/xfs_repair when you mount, then xfsdump.
dd conv=noerror,sync,notrunc bs=512 if=/dev/disk of=diskimg
See Also: http://xfs.org/docs/xfsdocs-xml-dev/XFS_User_Guide/tmp/en-US... http://xfs.org/index.php/Reliable_Detection_and_Repair_of_Me...
+1 for mentioning ZFS. It's really quite amazing. Almost like futuristic alien technology compared to the other freely available file systems.