In the military briefing room while discussing search and rescue, the map in the background shows a modern-day outline of Greenland. Whereas the motivation for their exploration was to explore its unknown boundaries.
(at around 43 mins) Iver cocks the rifle in preparation to shoot the polar bear. However, his rifle is already loaded as he was just getting ready to shoot a seal in the previous scene.
The rifles they use throughout the movie are Soviet built Mosin Nagant 91/30s which were introduced in 1930. At that time a danish expedition would have used Krag-Jorgensen Model 1894 rifles.
15:40 As the explorers climb onto the glacier one states, "It's like we've landed on the moon." While "A Trip to the Moon" came out in 1902, it did not depict an accurate surface. Telescopes did have some understanding of the craters since 1664; however, pictures of the surface of the moon were not taken until February 3, 1966.