From the release notes:
After you completed the upgrade to 7.0, the following bullet items may need to be addressed.
MySQL table upgrade is required after upgrading to ZCS 7.0. MySQL table upgrades are not automatically run during the upgrade to 7.0 based on time that it takes this process to run. There are no known performance impacts of running in production without doing this MySQL table upgrade. Customers can avoid these errors in the zmdbintegrityreport output by executing /opt/zimbra/libexec/scripts/migrate20100913-Mysql51.pl 

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Can I run this while the server is running, or must Zimbra be offline during this update?