Hmm, I don’t think that message is related to this plugin. It doesn’t do anything special with MySQL.
Are there any other logs in the WordPress directory? Depending on PHP configuration, sometimes messages can get logged in the wrong place if an errors happens before WordPress is fully loaded.
Also, what’s the memory usage of the site? The latest release uses slightly more memory than the previous one, so if the site was close to the PHP memory limit, installing the update might have been enough to push it over. You can use this plugin to view memory usage (it’s old, but it should still work):
https://www.ads-software.com/plugins/wp-memory-usage/
(Putting the numbers in quotes is not the correct fix, but that particular bug was only in 1.4 anyway.)