I was thinking this, but didn't say anything until someone else pointed it out. "Petty Officer" isn't really a class including corporals and privates. Petty officers are the naval/coast guard equivalents of Corporals and Privates, which are army/marine ranks.
I think it would be neat if the Maelstrom used Navy ranks, but since we're going with Corporal/Sergeant and private, they're not petty officers.
For an official source regarding US military titles, see:
http://www.defense.gov/about/insignias/enlisted.aspx
Furthermore, there is no such thing as a Private Third Class. It's just Private. Then you move up to Private First Class (marines) or Private E-2 (Army). I'm alright with second class, but calling someone "Private Third Class" seems more of an insult than a title.
Even if we continue to use "Third Class," I think there should be a "short title" used in dialogue. For example, instead of EVERY Adder-related NPC greeting me as Private Second Class Estheim, I think they should just say Private Estheim. Maybe Private First Class should be include in dialogue because it represents honour, but for casual conversation, the "Third Class" and probably "Second Class" don't seem appropriate.
If I'm not mistaken, the British army does have Privates classed 1-4, but I'm not sure if this is said/listed at all. I'd appreciate if someone with more knowledge of the Royal Army could help me out.