If the permafrost is melting enough for a mammoth carcass to be revealed, it must be summer, so there should be no night at all during the time period DCI Morton visits Fortitude.
Norwegian Police Uniforms don't have Canada Goose logos (nor any other producer's logo visible)
The Governor's helicopter bears Royal Norwegian Air Force markings, in addition to Danish civilian registry. Sysselmannen's helicopter on Svalbard has civilian Norwegian registry with no Air Force markings.
The vehicles shown in Fortitude have white registry plates with black lettering. Most vehicles on Svalbard have black plates with yellow lettering. Svalbard registered vehicles use the letters ZN and FH.