As for the character of Jack, I object to him because he's actually a bit of a vulgar stereotype (that and he's annoying). A true representation of gay people would be to have them just like everyone else, but of a different sexual persuasion. Jack, instead, is predatory and promiscuous, and talks in cheap innuendo and flirt. He's an obnoxious stereotype of a gay man.
You're making some rather dodgy assumptions here.
Jack Harkness is not supposed to be "a true representation of gay people", or any other kind of representation of gay people, really. He's a character, not a statistic. And yes, he is predatory and promiscuous, talks in cheap innuendo and flirts, not unlike, say, James Bond, whom - I'm sure you would agree - most people would not describe as a stereotypical gay man. He is also lively, enthusiastic, secretive and brave. In other words, like any other fictional character, Jack has flaws, habits and idiosyncrasies which make him unique. I don't see anything in him that I would call "stereotypically gay", except for the fact that he obviously digs guys.
I think he just annoys you for whatever reason, which is perfectly fine. But everything else is just after-the-fact justification.