With the help of someone who was experiencing the problem, I think I have solved the issue of the blank white tile in the woods.
The issue was that we told the game to draw a fully transparent image on top of the map tile; this was intentional as the way it was originally coded, it had to draw something (in other cases it draws a nearly fully transparent tile but with extra green trees to indicate the ways you can't go). However some interpreters & machines didn't like the fully blank .png file and were drawing it as white instead. Not fully sure why some were and some weren't but at least that's (probably) resolved.
As for the blank 4 direction tile in the dungeon, this still makes absolutely no sense to me. The walls image that gets drawn here is not different from all the other walls images in any meaningful way! But hopefully the breakthrough with the woods tile means that we'll eventually work out what's going on here.
I don't know the numbers but I'm also suspecting that most people who had a problem with the blank tile were experiencing the problem in the woods, not the dungeon. Please let me know in the comments section down below if this is true for you or not!
The crash to desktop problem is obviously not great but there's little I can do about it until we get some more insight as to what may be causing it. For those experiencing it, all I can suggest for now, is please save your game often! And try to work out any pattern at all that might explain what's causing the issue.