For those who are interested, the second error also happens here on meta - visit https://meta.discourse.org//t/posts-with-embedded-polls-fail-to-load/135549 as an example 
It looks like the basic URL parser spec says that a browser will always throw a validation error if a path starts with two slashes.
I suppose that one could argue that discourse should be checking that the path it is passing to history.replaceState() is valid before it does so and fixing it, but that sounds like a whole heap of pain (ie: implementing your own url parser and automagical fixer) for something which would be fairly rare in the wild.
This post has been brought to you by melted brains from reading WHATWG HTML living standards