>

As far as appearance goes, some might look the same under a microscope but then if you get a more powerful microscope, you may see a difference
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Yeah it's impossible to prove a universal claim like this.
But we can analyze water crystal formation and apply statistics and discover a rational belief. >

It's also weird that snowflakes get such emphasis. You could say the same about trees, or grains of sand, or pretty much any natural object >

Snowflakes are much prettier than those things.  Flowers could work, but then again 2 sunflowers look pretty identical often while snowflakes have distinctly different geometry. >

How "wide" is your definition of unique. 
Seems reasonable to suggest an identical shape with the same molecules is incredibly unlikely. >

Technically speaking, every snowflake is unique in the sense that the atoms that make up one snowflake are completely different from every other one to ever exist.  But as far as appearance goes, that might produce a different answer.