I needed to express that climate change and traffic congestion are issues that have implications for all inhabitants of the Earth. Therefore, I would really appreciate it if someone could tell me that whether "shared problem" indicate the same meaning that need or not.
Global warming and traffic congestion are shared problems.
Your initial wording is better. Climate change and traffic congestion are issues that have implications for everyone in the world.
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Climate change and traffic congestion are issues that have implications for everyone in the world.