Make sure that your init.d or upstart scripts to manage Unicorn and its workers are taken into account when capistrano-unicorn is doing the unicorn restart / reload / duplication tasks.
I did not think to look at these scripts when I had to debug the stale pid file / already running / unable to listen on socket errors. But it makes sense, as upstart starts Unicorn when it is not running, and then capistrano-unicorn is also attempting to start Unicorn.
I combine these capistrano tasks and hooks with Monit and a Unicorn init script.
Capistrano tasks:
namespace :monit do