Is there any way you can see what regions are unique?
Unfortunately no, "uniqueness" is not a property of resources. You know it yourself by remembering that when you make your scenes. Convention rules can help. One way to be absolutely sure is to look at the
.tscn file itself and see how many times the
SubResource( id ) is appearing, where
id is an index for that resource.
What I ususally do is to save AtlasTextures as
.tres anyways, so I can also edit them without having to open the scene where I used it, and it's easier to check where it was used by file search.
what would be the point of using an atlas that isn't unique per node?
Again, you use the word "Atlas" but I assume you mean "AtlasTexture", which is just a sub-region of a texture packed into a resource. The point of using such resources is being able to re-use them. If you need the same sub-region for something else in your game, you can pick up the same resource that you could have saved as a file beforehands.
Another use could be automatic spritesheet tools, which can slice an existing spritesheet and output a bunch of AtlasTexture files corresponding to each sprite in the sheet, which can then be used wherever needed.
Yet another use is the opposite: you could start with separate textures for everything, and ask a tool to pack them all automatically into atlases, replacing each property by generated AtlasTextures. This was an option in Godot 2.
Does having multiple nodes that use the same texture load the texture more than once?
Godot loads the resource once, but if more nodes need it too, it is cached in memory so subsequent loads cost almost nothing. This is partly why nodes share resources by default as well. If that wasn't the case, you would end up duplicating textures themselves, which would indeed cause big waste of memory.
Similarly, if you have 10 different AtlasTextures referencing the same texture, each AtlasTexture will be loaded because they all are unique, but because they share the same texture, that one will be loaded only once and not 10 times.