I am junior in a large corporation. I have been raising issues with management about problems with our products that may eventually cause some severe problems down the line - nothing life threatening but would certainly tarnish the reputation of the company and would result in serious financial loses.
My question is this, I have raised the issues with managers who oversee these things but their mentality seems to be its not their problem. They have no plans to fix the problems but that doesn’t sit well with me.
You say you are in a "large corporation" and are "going to management". However, you don't say who "management" is? Is it your immediate supervisor? If so, have you considered approaching your senior members of your team, your lead, or your immediate supervisor rather than "going to management".
When you approach these people, I think that the approach in the comments makes the most sense - instead of accusing or pointing out flaws, try to ask why things are the way they are. Hopefully, your seniors will see this as a desire to learn more and you'll come off in a positive light.
Ideally, it would be nice if "management" could explain why they are taking the approach that they are taking. But they have no obligation to invest time explaining company roadmaps or strategic plans, especially with junior employees. You are far more likely to make headway in your team, your immediate supervisor, or if you have one, a mentor.
Is it inappropriate for a junior employee to continue escalating issues to higher levels of management until someone decides to fix the problem? Will managers dislike me for doing this even if I have asked them to fix the problem before going elsewhere?
You have an ethical responsibility to various stakeholders. This includes not only the company and its employees, but also customers, users of your product, and the general public who may be impacted (no matter how indirectly) by the products your company makes.
You first need to take an appropriate and tactful approach for your company. Based on the wording of your question, I'm not sure that you have done that.
Ultimately, if you don't get traction and you continue to feel that this is a problem, you need to make the decision: do you understand the full situation and are you willing to risk your professional reputation by taking information to the appropriate authorities or, in extreme cases, disclosing confidential or protected information to the general public.