I would define a "problem" as anything that prevents a human being from having a long, fulfilling life with minimal suffering. Perhaps we could extend this further with immortality, but I'll leave that aside.
But if we consider that definition, then yes, there are many problems. They range from anything from physical to psychological needs. To feeling valued by society. To feeling fulfilled in relationships. All are "problems" IMO.
Because human beings exist in a social context, many of these problems boil down to a social contract between the individual and society. And discussions around the evolving nature of that contract in a way to minimize suffering is essential. With various philosophical problems like whether one groups increased suffering is OK if it minimizes average suffering.
For example, is it OK that we minimize the suffering of many in the near term by producing carbon? Knowing there may be longer term issues and externalities?
Is a war that will cause short term suffering OK if it liberates a group of people and may cause a decrease in longer term suffering?