Aharon,
Thanks for the more detailed info on the problem. I did grab the entire page source for the page you mentioned and processed it on my development server. The good news is that nothing in the content broke. In fact I ended up with a mirror of your page but with the external links info applied.
I do notice when I click on the link above the page takes a bit to load. A few things come to mind…
1) The execution time setting in php.ini is only set to 30 seconds (or a low value). I would try and increase that on the server (or have your host do that)
2) Check that php output buffering is enabled for your site
It simply seems that due to the page length, the server is just timing out the execution of WP given the amount processing going on. The added External Links time may simply be pushing it over the timeout setting.
In terms of the overall page length you might consider using the WordPress page break functionality simply to shorten the overall page length to a multi-paged post/page. From a user’s standpoint it is very long and takes a while to scroll to the bottom and back to the top.