1) Dry Law enforced in AMERICA (not: AMERICAN).
2) to popularize cockails THERE (not: IN EUROPE, it's a repetition).
3) I "feel" that it would be better to say "common AMONG the general public" instead of "common TO the general public": common AMONG, as in this case, seems more related to the "frequency" of something being present or happening (for instance a desease, or even a bad vice, like here), while TO seems seems more related to an IDEA, a BELIEF, or a FEATURE or something similar SHARED by many people.
Are there any English native speakers who can confirm or confute this?
4) You can't say (at the end of the passage) : ...became common...by the US military: something doesn't "become common by someone", but "is done by someone", therefore you could say for instance: "became common among the general public after having been spread into the country by the US military", or something like that.