Dr. NRG said:
What human was it that Tyrol most hated on New Caprica? Who was it he was leading a strike against? Who signed the death warrant for his wife? Oh yeah, the guy whose political philosophy he is now following, whose cell he is docilely visiting, and whose pawn he is now acting as. I just don't see it. Apart from that logic flaw, it wasn't a bad episode, provided you aren't an Ayn Rand fan.
Baltar-hate aside, Tyrol was the one who started out with the political philosophy on new Caprica. Baltar just happened to embrace it as his own. So it's not really Tyrol following Baltar, it's Tyrol following Tyrol and Baltar doing his thing, and the two happen to coincide on this issue. Baltar just happens to underline that belief Tyrol always had, and draw it out. Heck, even without that, Tyrol probably would have called for the strike when the kid got hurt.
Tyrol himself is in an interesting place, straddling both worlds Baltar describes. He's the Chief, head of all the mechies and techies, with all the benefits that go with it - he orders people around, he gets to do the jobs he wants with the people he wants, he can go drown his sorrows at the bar, he gets the single bunk/room with Cally that (for the most part) only officers get. There's also no doubt in my mind that a Tyrol would be Chief once Galen got old/died, just like Lee/Adama.
On the other hand, he's sort of an everyman. He's not a Viper jock or an officer, he's a grunt that has to work his butt off just like everyone else. He puts in long hours, and has to take crap from even the lowest Ensign, should they choose to give it. He gets very little credit for the normal work he does - his biggest credit was building the Blackbird, which was a collaborative effort anyway.
So, when he goes and visits Baltar, he's pretty much
the person on the show to get what Baltar is saying, to see it with his own eyes and ears. From one side or the other, it sounds like a bunch of crap - note how Roslin and Adama casually brush it off, even though he clearly has a point. Note how the workers decline to even accept any authority, or any rationale as to the situation. Tyrol can't do that, because Tyrol sees both sides every day, and that's why he has to be the one to see Baltar, to get him.
As an aside, Roslin's trick into getting Tyrol to talk later about the training wasn't her only dirty one. Putting Tyrol back in charge moves him further from grunt towards her group as far as status goes.