Even supposing the Thing didn't create the flying saucer it landed in, it has the ability to create a new one, so there could be Things all over the universe.
Well, the common theory is that Things get smarter mostly by assimilating knowledge from their victims, and Word of God is that the 2011 film was originally supposed to prove that the Thing was picked up as a biological specimen by an entirely different alien race. So, only the Things descended from the first Thing to crash on Earth would know how to build spacecraft; it's equally as likely that "Thingworld" has been quarantined — or sterilized — to avoid just such an outbreak.
The implication I got was that this thing was a virus spreading across the entire universe.
Luckily, since the last thing arrived 100,000 years ago, they're probably dead, at least near earth.
Originally this troper thought Window's lack of action against the Palmer!thing was just Windows being Too Dumb to Live — specifically, as the Thing continues its rampage in front of him, he simply stands there, not using his flamethrower. But then something occurred to me: has he crossed his Despair Event Horizon??
In the scene when Bennings runs to Childs, saying that "Mac wants the flamethrower", Childs replies with Flat "What.". Childs might just be figuratively saying what an awkward request it is. A fire alarm sounds in the background, the one which Mac turned on. Therefore, Childs up until this point has had a reason to think there is a fire somewhere, so his reaction is more like "What the hell does Mac need flamethrower for in the fire?".
Norris and Palmer immediately move in to extinguish the fires on the Dog-Thing after it drops to the floor, and we later learn it needs to burn for a while to make sure every cell is dead. They both turn out to be Things later on, so perhaps they were trying to save as much of their kin as they could without letting it look too suspicious.