What free or open source software can I use with Mac hardware to verify integrity of every block of a disk where Core Storage is used?
Install badblocks on Mac OS X (Leopard or less)

Mac OS X Ext2 Filesystem includes a badblocks that can be used with Mac OS X. 

Credit: doctormac: How to check for bad blocks on a mac with Mac OS X? (2011) reference to Bad blocks? badblocks! | Terminal (2007)