I have seen this problem on a lot of posts and the main reason seems to be white space. The posts I have seen usually include some plugin file or header/index.php file.
So this is the full story - I have moved a site to a new server, hosting company. The blog seemed to be working fine after the move, I updated to the latest version of WordPress, 3.8.1 I believe and updated plugins and themes (there are only 3 plugins in total on the site).
The problem occurs for me when I update/publish a post.
This is the full error I am getting (after I have changed 'WP_DEBUG' to 'true'):
Notice: automatic_feed_links is deprecated since version 3.0! Use add_theme_support( 'automatic-feed-links' ) instead. in /usr/local/pem/vhosts/236304/webspace/httpdocs/xxx.ie/blog/wp-includes/functions.php on line 2908
Warning: Cannot modify header information - headers already sent by (output started at /usr/local/pem/vhosts/236304/webspace/httpdocs/xxx.ie/blog/wp-includes/functions.php:2908) in /usr/local/pem/vhosts/236304/webspace/httpdocs/xxx.ie/blog/wp-admin/post.php on line 233
Warning: Cannot modify header information - headers already sent by (output started at /usr/local/pem/vhosts/236304/webspace/httpdocs/xxx.ie/blog/wp-includes/functions.php:2908) in /usr/local/pem/vhosts/236304/webspace/httpdocs/xxx.ie/blog/wp-includes/pluggable.php on line 896
I am not sure what to do now, I have looked in those files and don't see anything out of the ordinary. I was thinking of replacing the wp-admin and wp-includes folders with the latest version of WordPress manually to see if that helps.