That's a complex question with no simple good or bad as an answer.
Factors that were important INCLUDE:
during that era there was less that medicine could do for people because this is basically pre-antibiotics, and health care back then didn't look like what it does today--no high tech anything for sure. (Note for those who know medical history, yes right before 1900 penicillin was known, but we tend to go with Fleming's 1928 work. The Great Depression started in 1929. Ehrlich's Salvarson for syphilis wasn't going to help with TB or other concerns for that time period, etc.)
Anyway, back then health insurance did exist but was not common. Blue Cross was essentially the forerunner in the field:
"Born out of necessity in the Great Depression, the Blue Cross concept was created in 1929 by a pioneering businessman, Justin Ford Kimball. He offered a way for 1,300 school teachers in Dallas to finance 21 days of hospital care by making small monthly payments to the Baylor University Hospital.
Around the same time, the Blue Shield concept was growing out of the lumber and mining camps of the Pacific Northwest . Serious injuries and chronic illness were common among workers in these hazardous jobs. Employers who wanted to provide medical care for their workers made arrangements with physicians who were paid a monthly fee for their services.
These pioneer programs provided the basis for what would become the “modern” Blue Shield Plans."
http://www.bcbs.com/about/history/blue-beginnings.html You can see there was a limited coverage group during the Depression.
Physicians historically have helped those in need and many treated people for free or took something in trade (like food).
Hospitals existed, of course, but there really wasn't much by way of insurance for them at that time (more of a circa 1934 event--see
http://www.ohiohistorycentral.org/entry.php?rec=852&nm=Blue-Cross-and-Blue-Shield-Mutual-of-Ohio&PHPSESSID=57168c4333adf4ae127ff54cb2bc1367). (Another early plan was 1936:
"In 1936, the collection of business leaders pooled their savings and launched a non-profit company called Hospital Service Corporation. This company offered an affordable pre-paid hospital plan which, at the time, was a new concept. The plan quickly became known as "the Chicago Plan" and was one of the forerunners for today's concept of health insurance. The idea behind the Hospital Service Corporation caught on around the United States and gave birth to Blue Cross and Blue Shield of Illinois, as well as Blue Cross and Blue Shield throughout the country."
http://www.insuranceusa.com/directorycontent.php?id=BCBS_of_Illinois) Here's an example from one long-time hospital that is representative to the best of my knowledge: "The hospital struggled to make ends meet during the Great Depression. Decreased salaries and no-pay and shortened vacations for the nurses came with the bad economic times.
Concerned citizens donated fruit to the hospital's kitchen. Nurses canned peaches and pears during the evenings. Dedicated employees with a teamwork philosophy, continued Lakeside Hospital during these tough years."
http://kpcnews.net/special-sections/reflections2/reflections27.html In other words, with such a huge percentage of the public out of work and limited funds available essential services (like health care) could be the result of folks pitching in--the staff, the community, etc.
So people kind of muddled through. There were things that definitely affected health back then, so I'm not saying folks were not sick or injured or that if so they automatically got the treatment they needed. But back then factors that would particularly affect health would include:
malnutrition--yes people actually DID go hungry back then in many cases and the norm probably was inadequate nutrition
ravages of temperature extremes--the Depression lasted for years--electric and gas companies DID shut services off if not paid for and people went through bitterly cold winters and ferociously hot summers with little by way of temp control. Air conditioning was pretty new back then as well.
public sanitation was not always great because when masses of folks were on the move the country was not set up for that to put things delicately. One of the first things anyone who really knows public health will tell you is you need proper sanitation methods and clean drinking water and those were not always where masses of folks congregated.
Remember too that vaccinations were relatively recent (and yes I do know when Jenner lived, but it's more Pasteur on that we see real numbers of vaccinations.)
So overall, living conditions for large portions of the population were bad: inadequate nutrition, uncomfortable crowding, sanitation issues, basically pre-vaccinations and pre-antibiotics time frame, and you did whatever work you could get so there were injuries as some of it was dangerous and sometimes people weren't well and that leads to accidents.
Health care existed but was spotty I think would be fair to say. I would say docs did what they could but resources were limited and medical science was less developed than now. Hospitals existed but care was problematic (costs, staff, resources).
Hope that helps some.