it severely depends of the context used, but on a glance this can mean that whatever immediately caused it, the source of the problem are wider. For example, if a teenager robs a shop you can say that he did it because he is a bad guy, or you can broad your view and look up to his family, school, peers, society as a whole, etc. In this case, i can imagine a dialogue like A "I think he did it just because he is nasty" B "I think this is a broader problem, instead". it may not refer necessarily to a more severe or serious problem, but just various sources that added together make the "problem" happen.

Now, the group that defines mental illness in America is thinking about redefining narcissism.Nothing's been decided yet, but there's a good chance that Narcissistic Personality Disorder[ NPD] will cease to be a mental illness of its own and will instead be folded into other personality disorders, making it a trait of someone with 【a broader problem】. This means that this person with NPD will probably be seen as having another mental illness as well

broad v. narrow Some topics are broad, others are narrow. Some minds are broad, others are narrow. A broader problem = the problem is broader than people think it is.