Based on the first link, it seems as though zero and upper-case "O" are very similar. (My eyes cannot discern a difference, but I admit that my eyes are not top-notch.)
The original typewriter had no "0" or "1" you were expected to use "I" or "O" in place. I suspect an authentic typeface should have trouble distinguishing them.
and having said that, forget authenticity, I really appreciate typefaces that make an effort to distinguish all characters.
Old Timey Code fixes both of these-- it has a slashed zero and redraws the number 1 to be distinct (angles the top serif).