Full record url in nginx log

Try adding the $host variable in log_format:

log_format main '$http_x_forwarded_for - $remote_user [$time_local] "$host" "$request" '
            '$status $body_bytes_sent "$http_referer" '
            '"$http_user_agent" $request_time';

http://wiki.nginx.org/HttpCoreModule#.24host:

$host

This variable is equal to line Host in the header of request or name of the server processing the request if the Host header is not available.

This variable may have a different value from $http_host in such cases: 1) when the Host input header is absent or has an empty value, $host equals to the value of server_name directive; 2) when the value of Host contains port number, $host doesn't include that port number. $host's value is always lowercase since 0.8.17.

If you want to log the full requested url, then my method is

log_format main '$http_x_forwarded_for - $remote_user [$time_local] '
'"$request_method $scheme://$host$request_uri $server_protocol" '
'$status $body_bytes_sent "$http_referer" '
'"$http_user_agent" $request_time';

So splitting the $request into its constituent parts and popping $host in the middle. Also lets you see if the request is http or https.