we're getting girly here.

We are...?

oh, no. I was confusing Heroin with Heroine.
Getting a little druggy here, aren't we?

Actually Captain is his American Army Air Corps rank, as he is an American volunteer that has been sent to Britain, likely part of the RAF Eagle's Squadron which was made up of American volunteers.

He wouldn't have been referred to as Captain however, as the Eagle Squadrons were under the jurisdiction of the RAF and used their applicable ranks. Jack would have been a Flight Lieutenant as his equivalent rank, though he wore the insignia of a Sqaudron Leader in his first appearances, meaning his USAAC ranking would have been Major. In Torchwood he wears the insignia of Group Captain which would have made his USAAC ranking as Colonel. In the Lahore flashback of Torchwood he was wearing the three pips of a UK Captain, the only possible way he could have gotten the title.

It's really just one huge continuity mess that can't easily be resolved.

A big mess indeed...

Thing is they just made it worse by trying to fix it, like giving him the "Group Captain" badge and stuff.

Yeah cause even if he was a Group Captain then they wouldn't call him Captain.