Comments from Vault.
 

How do I pull commits from vault about the updated files in source control and dump them to a log file?

Also how is this handled when there are multiple updates to a file between builds?

Perhaps the history or listalltxdetails command? SourceGear support is probably a better source for a more definitive answer.

To log a Vault step's output to a file, enable file logging in VBP, or use a Write File action following the Vault action and log %LASTSTEP_OUTPUT%.