I just discovered that it's dark where all the studs are on our interior walls facing outward. It almost looks like ash or smoke stains, see attached pictures. It's more visible on some walls. It doesn't seem to matter what facade is on the walls because we have brick on some and wood on others. The house was built in '68. Is this moisture, and how has the moisture gotten into the walls?
Now I can't see the pictures. But in our house built in '75, it was allowed to skip the air gap in the outer panel (if that's what it's called), so on our street, many have gotten moisture and mold damage. But it doesn't have to be so in your case.
It is probably not moisture but ash from the pellet burner. The stains disappear when you wipe them away and the cloth gets dirty. It is a bit difficult to wipe them off as it easily darkens the surrounding area, so we might have to paint all our interior walls.
It is likely a thermal bridge in that corner where dirt sticks (thermodiffusion - particles are attracted to cold surfaces, i.e., the studs and especially the nails). It's difficult to do anything about it without changing the construction, i.e., breaking the thermal bridge. However, this is not an indication of moisture in the construction.