I have a theory to explain the massive blood loss Jack sustained during the last episode. I believe that the time travel has something to do with it. Jack stopped aging, and for that to occur his cells must multiply at an accelerated rate to keep him young like that. I think Jack has a healing factor. Not as powerful as Wolverine, but more like Captain America's. He can regenerate superficial cuts in a matter of minutes, and can recuperate from more severe wounds such as gunshots in days. That makes sense with what we've been shown; Jack healing a nice to the side in a few days with barely any medical treatment and healing some cuts during in the fight between shots.
Just a theory, don't take it too seriously.