This is extremely cool, although it's a little unnerving to see people working with so much lead with bare hands, especially considering a lot of them had the job for decades. Was lead poisoning an occupational hazard among typesetters?
Beyond hunting, the military is moving in the same direction; the Army has switched to using lead-free bullets as its standard rifle ammunition (https://www.americanrifleman.org/articles/2014/5/21/testing-...), for example.
In addition to those mechanisms, I think another popular one is cigarette smoking. If you were handling lead, it could get absorbed into the cigarette and inhaled that way.
People are surprised how industrial the process used to be, and how tough and unregulated industrial jobs were back in the 70's and the decades prior. Our guide told us that in the old NY Times building (the one shown in this film) there was a hospital on the 13th floor for people who got burned or (his word) mangled during the hot type process. The New York Times had doctors on staff for printers who got hurt badly enough that an ambulance ride uptown would take too long.
A couple of the workers in the movie are wearing paper hats. That's to keep ink that's floating around in the air out of their hair. No masks! But at least their hair would be clean.
The real danger in the newsroom is in the hot metal press, because you've got hot metal (likely causing some problematic airborne lead) running around at high speeds. The composing proofs themselves are going to be very minor in comparison to the linotype and printing machines, which are going to be occupational safety hazards for sure.