Loved this film when I first saw it back in 1999, and although I think it is still good (first time is always the best with a film like this), John Carpenter should have had an idea who was infected an by what means for continuity purposes. Once upon a time I would have agreed that it was supposed to be Palmer's shadow we see when the dog walks into the room.
However, in a subsequent scene we Palmer light up a huge spliff in his mouth, then pass it onto Childs. Sometime later on Fuchs explains that it only takes one molecule of The Thing/Creature/Alien to assimilate an entire organism and therefore recommends that each person prepares theirs own meals/drinks and only eat from sealed cans. If this is true, and Palmer was indeed the first to be assimilated by the dog, then that means that Childs was also infected, except the subsequent blood test proved that he was human.
So, this means that it must've been Norris' shadow we saw and he was (presumably) the first to be infected by the dog (a possibility as the shadow looks like it could be Norris or Palmer), either that or it was Palmer's shadow and he wasn't assimilated until sometime later on (which I highly doubt) or the third possibility is that is was Palmer's shadow but the filmmakers made a continuous error because even they didn't think about who, and when, and how each character was assimilated, or they simply forgot about the information what Fuchs would later reveal from Blair notes.
As for Blair, I think he was assimilated sometime after he is 'Quarantined'/isolated in that hut, as The Thing had ample opportunity to attack and assimilated someone who had been segregated and isolated from the rest of the group.
