As part of my research into the art style, I found an online copy of the first Superman story. I can see why some people were upset with the violence depicted in the strip: some of it is pretty seamy. The setup for Superman's origin is as flaky and fractured as it is simple and endearing. Authors Joel Shuster and Jerry Siegel seemed much more interested in action and results than setting up plotlines or establishing characters. Under a crushing deadline, they worked fast to cobble together whatever they could for their first publication.
The closest thing to a plot involves Clark Kent, Lois Lane, and some lascivious mobsters, and it leads to the fantastic image on the cover. Mild mannered reporter Kent works up the courage to ask Lois out on a date, and to propel the plot she reluctantly agrees ("I suppose I'll give you a break," Lois tells him, "... for a change."). Unfortunately, mobsters lust after Lois on the dance floor and not only cut in on hapless Kent but kidnap Lois. Unable to defend his date, Kent relies on his alter-ego Superman to save the day. Superman chases down the mobster's car and shakes them out like dice from a cup. Then in anger and revenge, he smashes the car against a nearby rock. Later, he sorts out the mobsters and safely escorts Lois Lane home, where she discovers that nobody will believe her story.
If you were never acquainted with the Superman origin before, now you know the story behind the great picture on Action Comics No. 1. It's also precisely the same story as Action Hamster No.1, except with rodents.