Bullitt - Plot Question

[Iguanaman]

Hi,

I just watched Bullitt last night - not sure I'd ever seen the entire
thing - and it was great. Not just the car chase (which is fantastic),
but the whole movie. But I found the plot confusing. Can somebody
clear up my questions, please?

Okay, the guy shot in the crummy hotel room is not the mafia witness -
he's a decoy who's been setup by the real mafia guy who wants to escape
to Europe. Somebody tipped of the organization, and they shot the
decoy, not knowing of the ruse. Bullitt wants to know how the hitmen
knew where to go - somebody tipped them off.

I thought, at first, that it was Chalmers, that it was all a setup by
him and that he was somehow getting paid off by the mob, but it seems
at the end that he's just an oily politician who's only concern is for
his public hearings, etc.

So, who did tip them off? And didn't somebody tip off the mafia guy to
where the wife of the decoy was staying? Wasn't it the police guy
played by Norman Fell? He was there when the location of the wife was
mentioned, then when Bullitt requests a car to get out there, he's
told, "No cars available," and he sees the Fell character driving away.
Next thing, he's looking at the body of the decoy's wife.

This was never developed in the plot - are we supposed to have caught
that and left the film feeling that the bad guy got away, and remains
in the police force undetected? Pretty rough! But nobody comments on
that in reviewes, so I'm wondering if I missed something.

Thanks!