It's hard to see any "black spots" in your pictures. Can you shoot a close up?
I have several "spots" on the seat of my saddle where mice have pooped on the leather and the acid in the feces "marked" the leather. I've cleaned it but it'll never go away. I just take better care to store my saddle in a safer place now.
It's been damp and had a type of mould at some point in its life. Unfortunately these spots never go away but eventually they'll fade into the general patina of the leather. Very common problem, unfortunately, especially with brown tack because it's more noticeable.