You Should always disable front-facing errors on live sites for security reasons - regardless.
If you want to hide the errors in Wordpress and get a log of the errors for review instead, you can do something like the following in your wp-config.php file:
// Enable WP_DEBUG mode
define( 'WP_DEBUG', true );
// Enable Debug logging to the /wp-content/debug.log file
define( 'WP_DEBUG_LOG', true );
// Disable display of errors and warnings
define( 'WP_DEBUG_DISPLAY', false );
@ini_set( 'display_errors', 0 );
PS: If you want to use the remove_action code by alexg above, remove_action('shutdown', 'wp_ob_end_flush_all', 1);
you will need to place it in the functions.php file of your theme.
PPS: You may also want to try using define(‘WP_MEMORY_LIMIT’,’1024M’);
in your wp-config.php file - however, be careful that you don't allocate more than you need to as this affects the front end of Wordpress and you'll run the risk of running out of RAM if you have too many simultaneous hits on pages.