"Cover the waterfront" had significant drift of the signified (or "meaning creep" if you like a less technical term) even in the 30s and 40s.
Newspaper slang in the 20's, when it was confined to the journalism world, meant "I work where I see and write about a little bit of every kind of news", which at the time meant violent crime, vice, smuggling and other mob operations, sea tragedies, labor strikes, war preparations, construction projects, etc etc etc. (See Dix Harwood, Getting and Reporting News, one of the first J-School textbooks)
By extension after the movie it was used to mean "I am responsible for and know something about a wide range of things."
But the song was about someone hanging out where ships come in, hoping for the return of a lover. Then by the late 30s it was beginning to be applied to exhaustive reports and long detailed presentations, and that meaning became more common during WW2 and the Cold War (which ran on long presentations).
But all the meanings continued in use; the Orioles had a big hit with the song, "I cover the waterfront" in its original sense was still occasionally in use at magazines and in some academic disciplines in the 1990s, and of course when you hear it used today it's more commonly in the defense/corporate sense.
That's at least 3 possible meanings for a phrase that may not be familiar at all. I think this is one of those like "decimate", "beg the question", "oil on troubled waters", or "toe the line" that is better avoided in new writing if clarity is your goal.