When Illya and solo surface the water in their scuba equipment, the chunks of ice-berg surrounding are clearly Styrofoam, and the ice-berg where the Eskimos are situated looks acrylic.
The inside of the igloos are clearly props. Blue lines are painted to show the separation of the carved slabs of snow.
Illya and solo emerge from the water with bare hands, which would be impossible to do in the frigid Arctic water.
Many of the characters routinely walk outdoors wearing regular clothing in what would be freezing Arctic temperatures.
Murphy says she graduated from McGill University not McGill college.
When Kuryakin frees Solo by throwing the knife at the rope, not only does the knife strike the target before he throws it, it was thrown from a different angle.
When Illya is showing breathing apparatus to Napoleon he has his attached upside down (red to his right). Looking at the writing on the device Solos is correct (green to the right). Either way, one of them is in trouble.