What's the fastest way to execute a MySQL Dump of a large Database?
Set up the OS with LVM Snapshots.  Preferably have MySQL in a separate partition or drive that is to be snapshotted.  Then to take a dump:


Stop mysqld
take snapshot (a minute or so, regardless of dataset size)
start mysqld


Copy (suggest rsync) the snapshot to the other machine (this takes time) into an identical snapshot area.


start mysqld


(Caveat:  I have never tried this, so there could be some rough edges.)