Comment 8 for bug 1637701

For the sake of completeness maybe "dpkg --verify mysql-server-5.7" ?
To check for accidential changes?

But I'd expect the issue to be more around: /var/run/mysqld/mysqld.sock access issue.
And that appears to me to be more of a fail-to-start server issue, and due to that the upgrade not being able to reach it.

Normally on mysql bugs there is also an error log of the mysql server which is missing here.
This should have much better info why the server failed to start.
http://askubuntu.com/questions/812001/how-to-see-mysql-error-logs