Early in the film Charlie's girlfriend Estelle takes a photograph of Charlie and his fellow pilots. When the photo is snapped Charlie is clearly inhaling a cigar and has his eyes closed. Later in the film this photo is presented to Charlie's boss but the cigar is absent, his eyes are open, and he's smiling.
With catastrophic engine failure, aircraft (particularly 1940's Norseman, built specifically for rugged bush flying) don't generally lose steering control. The failed engine, after blowing a head gasket would shut down almost immediately, not continue to run. The aircraft would glide with stability even though the engine wouldn't be running, and it wouldn't be very difficult to control, because the engine systems are completely separate from the cable/pulley control-surface systems.
When is snowing, where the plane is crushed, the snow doesn't touch the water. The water isn't disturbed.
After the caribou hunt, Kanaalaq coughs up blood. Before she coughs, you can see the bulge in her cheek from the fake blood capsule.
An instant before the plane finally crashes down into the water, you can see a small fiery explosive charge go off at the tip of the tail at the top of the screen as the cable holding the plane up is released.
The Buck Knife that Charlie relies on throughout the movie was introduced in 1962.
The movie takes place in 1953 and the Charlie comes riding in on a Harley Davidson made after 1970.
Later in the movie when Kanaalaq's condition worsens, Charlie says he will have her Medevac'd to a hospital. The term "Medevac", (meaning Medical Evacuation) was not coined until the Vietnam War.