Uh huh. \derisive
I think this all comes down to the claim that their "memcomputing" architecture allows you to put exponential amounts of data into a polynomial number of things. My best guess for where they went wrong is something like measuring an exponentially small voltage difference.
A good rule of thumb: if a proposed thing violates well-known bounds, like say the Bekenstein bound [1], and the authors don't mention this at all, that is not a good sign.
The paper would probably be fine if they took out everything implying that UMMs can be physically instantiated, but I dunno.