A reef tank will always have a slight *bait* odor to it, although I know what your talking about. eventually the tank should have a slight fish smell that smells believe it or not *sweet*
I suspect that you may not have adequate circulation. What's this that you're running the skimmer "half the time?" You really want to run it always. As I always say... you're better off removing as much as possible and then re adding via water changes and feeding with the homemade food mix, rather than worrying about running the skimmer 1/2 the time because your worried about removing too much.
You don't say how much or often you add kalkwasser? You should use it full strength freshly made, for all make up water.
I would
I've never experience the musty odor unless the water was in an enclosed vessel such as a covered bucket or garbage can. I don't it matters how cloudy the kalk water looks when mixed, all that matters is the calcium level raises when you add kalk. Have you tested the tank water before and after adding?
Does the musty odor occur rite out of the filter or is the water in an enclosed container?
I don't think its anything to worry about, providing the ca is getting elevated in the tank.
Hope that helps Robert