Linked tables change during dump
InnoDB?  Or MyISAM?  Or a mixture?

If MyISAM, why are you not moving to InnoDB?

Look at the arguments to mysqldump.  One says to lock all the MyISAM tables for the duration of the dump.  (This, of course, is nasty for updates/inserts.)  Another says to "lock" InnoDB tables as a --single-transaction.  (This is not so nasty.)

Xtrabackup (see percona.com) is an alternative to mysqldump and an excellent way to backup a live system of InnoDB tables.  So is MySQL Enterprise Backup ($$).