What kinds of problems did labor unions want companies to address?
That depends upon which era you are talking about.
The earliest labor unions go back to the 1830s when "mechanics" banded and the women of New Hampshire and Massachusetts sporadically banded together. They plight was usually over working conditions and seldom about pay.
Early post civil war farmers of the plains banded into the Grangers, more a brotherhood than a union, but still worked in common cause, keeping the plains open, not barbed wired.
In the early 1870s the Knights of Labor was founded to provide skilled laborers with a platform to address grievances against particular mills. This too was general over working condition but wages did occasionally enter in.
In the 1880s and 1890s the United Mine Workers, an independent union. always struck over working conditions in the mines, too many explosions, cave-ins and other hazards. They almost always lost by-the-way.
In the early 20th century the focus turned to number of hours worked and wages, almost as a single issue. This was handled by the recently formed American Federal of Labor, AFL, but only for skilled laborers. The Industrial Workers of the World, I.W.W., a socialist group, took on the plight on unskilled laborers but took on skilled laborers as well. At that time mill operatives were expected to work upwards of 60 hours a week at 7 cents an hour and had no expectation of job security. Also, and depending upon the state, children as young as 8 were employed in mills and required to do dangerous jobs.
The 40 hour work week is the result of labor strikes in the 1910s, as were the child labor laws. Children under 14 not allowed to work.
Most of the early 1920s forward and to the 1970s strikes were over wages and benefits.