After screwing around a bit, I found the answer myself.
The problem was apparently, that if you plug a vector value into the base color, none of the R, G or B channels can be 0.
This is what happened when I plugged in a normal texture. Anything hit by light goes black and gives artifacts;
However, when I added an additional value of 0.01 to each of the RGB channels of the texture, it changed into this (don’t mind the shadows being white; that’s just me not having finetuned the scatter, specular and whatnot settings). As you can see, the artifacts are gone and the whole thing renders quite nicely.
Pretty sure it’s a bug.