In the cave, they find a metal viking helmet in the water. Any archaeologist will tell you that water will not preserve metal/iron at all.
When walking through the forest to get to the lake several oak trees are visible in the background. As this movie is set in Finnmark on the border toward Russia the climate is too cold for oak. This indicates the scenes have been shot further south.
The island in the Eye of Odin is not very high, but the cave is very deep. The level of water in the cave should be much higher.