Solution:
https://forums.zoneminder.com/viewtopic.php?t=24265

Two tweaks must be applied.

Part 1

In the web interface, go to options -> paths, and update PATH_ZMS from “/cgi-bin/nph-zms” to “/zoneminder/cgi-bin/nph-zms”

Now, I get the following errors in the apache error log:

==> error.log <==
[Tue Feb 09 15:33:23.463262 2016] [cgi:error] [pid 1278] [client 192.168.0.222:62826] script not found or unable to stat: /usr/lib/cgi-bin/nph-zms, referer: http://192.168.0.13/zm/index.php?view=watch&mid=1

Part 2

We must now fix the pathing in apache to match the above configuration

edit /etc/apache2/conf-available/zoneminder.conf
#ScriptAlias /zm/cgi-bin "/usr/lib/zoneminder/cgi-bin"
ScriptAlias /zoneminder/cgi-bin "/usr/lib/zoneminder/cgi-bin"

Finally, restart both the web server and the video monitoring software.

service apache2 restart
service zoneminder restart