The very first time we see Kate, when she is examining the extracted specimen, she is listening to music on molded plastic headphones that were not available in 1982. Smaller headphones such as these, designed at the time for listening to Walkman-like portable equipment would have had a metal band going over the head, holding the earpieces in place.
Near the beginning when flying to the Antarctic base, Dr. Kate Lloyd (Mary Elizabeth Winstead) is shown flying in a helicopter without hearing protection or headphones (one of the characters motions her to put them on so they can converse). Flying in a cargo helicopter is painfully loud (120db or higher) and there is no way that anybody could fly in one for hours without protecting their hearing. In fact, it's mandatory on the majority of flights
The dog in the final scene (intercut with closing credits) has inconsistent coloration because two different dogs were cast. The initial escape shots were filmed in 2011 and the subsequent aerial shots were taken from the John Carpenter film The Thing.
In the 1982 John Carpenter version, the Americans watch the videotape shot by the Norwegian team. They clearly show them outlining the Thing's spaceship through the ice, and then attempting to dig it out with thermite charges. We then see the video of the ship exploding. In the 2011 prequel, we do not see the ship explode.
When Lars is guarding the helicopter pilots, he yells at them a line in Norwegian which the subtitles mistranslate as, "Don't move, demons". An accurate translation of the line would be, "Take it fucking easy".
Dr. Sander Halvorson speaks fluent Danish without an accent to his fellow Norwegians. Actor Ulrich Thomsen is Danish.
Danish and Norwegian people can, for the most part, understand each other. In some cases there might be a confusion, as the Danish language can be hard to follow, but this still doesn't qualify as a goof.
When Kate Loyd is inspecting the mouths of her colleagues for fillings she appears to be using an LED flashlight which did not exist in 1982. It was not an LED flashlight. It does look like the beam from the light is touched up with special effects to make it more apparent, but this is not a goof.
The Thule Air base is not Norwegian. It is located in Greenland and is a U.S. Air Force base. However, it is a fictional base in a fictional movie. Therefore not intended to be the real Norwegian camp in Antarctica.
In the 1982 film, we see a videotape of the Norwegian crew (the crew in this installment) blow up the ice-layer on top of the spaceship with dynamite, yet in this film they don't blow up the ice-layer.