Firstly, in my opinion, the film would be exceedingly middling without the fantastic practical effects on display. That is, if the alien were CGI, I feel the whole thing would be exceedingly meh. The plot and characters are decent, but not exceptional. The film does succeed admirably in creating mood and tension, but I feel this is as much due to the creature effects as anything. This isn't to knock Carpenter's directing or the soundtrack, both of which are excellent, but if The Thing were released today with the standard computer effects, I doubt it would attain the cult status that it has. Perhaps the 2011 re-remake will test my theory, assuming it doesn't suck altogether.
This isn't a knock against The Thing. There are a great number of excellent movies that would be hugely diminished if their practical effects were removed: 2001: A Space Odyssey; King Kong (1933); Team America: World Police. At the time though, The Thing received critical flak for having too much style over substance, and I feel that our opinion on the film (currently 80% on rotten tomatoes) has morphed partly due to ennui over CGI and a collective nostalgia for physical objects.
Overall, I think that CGI has improved the medium of film by making it possible to show almost anything at an acceptable cost. This in turn affords screenwriters more creativity, and consequently more films with fantasy elements are being released today than ever before. The problems come when directors and studios come to see CGI as a panacea, forgoing all other types of effects. Plenty of films, even horror films like Drag Me to Hell, use CGI heavily and are better for it. Then you have Peter Jackson's King Kong, which features excellent locations done in miniature, and dinosaurs that look worse than Jurassic Park, a film that came out twelve years earlier. I think the rule of thumb should be this: if it's magic or something ephemeral, use CGI, if it's something physical, strongly consider some sort of practical effect.
But getting back on topic, while the pacing and atmosphere in The Thing work well, the plot has a few issues, and I want to bring up the most major problem I had, and please keep in mind that no normal, well adjusted person would be as bothered by this as I.
A certain ways into the movie, the characters collectively realize that the alien is taking human form. To ascertain whether one of them has been taken over, the doctor proposes the idea of a blood test. They'll each donate a sample of their blood, and each in turn will be mixed with a sample of regular emergency blood that they know to be untainted. Based on previous observation of the interaction between alien cells and normal cells, if a reaction occurs, then that donor is infected. This plan is scrapped when it is discovered that blood bags in storage have been tampered with (e.g. they have tentacles growing out of them).
The issue I have is that with the established fact that alien cells react with normal cells when the two are mixed, the previously described experiment could easily be performed without the uninfected blood bags. What the characters need to do is mix blood samples between every combination of two people. If there is a reaction, then one of those two people is an alien. After running through every combination, based on who reacted with who, you could divide everyone into two groups, Group A and Group B. Everyone's blood would react with all members of the opposing group, and with no members of their own group. As is stated at one point in the film, the infected must not outnumber the uninfected, or else they would simply reveal themselves and overpower them (ala Werewolf/Mafia). Thus the smaller group are the ones infected, and they may be promptly disposed of by the larger group.
Also there are no shape-shifting aliens in Antarctica, so there's that too.