Been reading through the thread and great work!
leather is fun...
In terms of the black line/water stain, it depends on the dye you used. Water based might smudge out with a dampened cloth but its unlikely and definitely tricky not to just move the stain round a bit. Oil based dye leaves you with not much choice other than to leave it or re-dye it as far as I'm aware. Either way, I'd just embrace it and get a nice patina on it; let time do its thing.
After all, if you really really don't like it, then I guess it can be a reminder of a lesson learned :') but I quite like it personally.
Again, nice work; glad you're enjoying it and thanks for sharing!