The immune system is an example of how Every Solution Brings a Problem.
The immune system has a first-order problem to solve: bacteria, viruses, and parasites. It has a variety of mechanisms to do that, developed via a Red Queen's Race 
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But these solutions have caused a new class of problems, auto-immune diseases, where the mechanisms used to protect the body attack it.
Auto-immune diseases have solutions of their own, which is part of the reason Your Body is a Gross Kludge.