How private is the "Private" network?

Other Linodes aren't going to be able to spoof your IP or sniff your traffic - however, all Linodes on the private network within a given datacenter are on the same network, so in a sense it is not fully private. If you have services listening on a private IP in Newark, and I scan that address from one of my Newark Linodes (that also has a private IP), I can see what ports you're running things on, etc.

If you're worried though, you should consider firewalling + some kind of service-level encryption.

The most important issue for me, is traffic sniffing because the load balancer (haproxy) terminates SSL connections there. The rest (open ports) are irrelevant because everything is behind firewalls that allow connections from known private IP addresses.

It is very easy to use Ansible for updating a list of private IP addresses within the firewall of each server.

It is not possible for Linodes to receive traffic that is not destined for them, so the only one able to sniff your traffic is Linode. But as smallclone says, if you're worried, you can always encrypt your traffic.