I just assume that every historical movie contains inaccuracies. Narrative reasons, budget constraints, dramatization, ... I don't always agree with the creative choices, but I understand why they do it and I'm not going to let it ruin my viewing experience. I can always jump into a wikipedia rabbit hole after the movie.
I can only think of one movie where they went too far for my tastes: the Hollywood movie where it's USA soldiers who capture an intact enigma machine from a u boat.
That said, the danish military was involved in the mine clearing, only not in the way how it was depicted in the movie. https://commons.lib.jmu.edu/cisr-journal/vol22/iss1/4/ The actual pdf contains a better description of who did what than the abstract.
If they were giant smokestacks further back, then they would be in the haze of the smog, like everything else in the background. There's a similar vertical object visible in the top right corner, far back and obscured by the haze, but I think it's a chimney just like those in the front.