I had Jetpack running on one of the sites in a Multi Site network install but since I
1. started using the contact form feature on that site and
2. activated this plugin network wide,
I started seeing these messages in the error log:
PHP Notice: ob_get_clean(): failed to delete buffer zlib output compression in /var/www/wordpress/wp-content/plugins/jetpack/jetpack.php on line 735
PHP Notice: ob_end_flush(): failed to delete buffer zlib output compression in /var/www/wordpress/wp-includes/functions.php on line 2571
No idea if and which one of the two things I did are related to this.