Significant amendments in the UPSC syllabus relate to Indian law include updates on the Constitution, amendments in criminal and civil laws, and contemporary legislative changes affecting governance. Recent additions focus on human rights, environmental laws, and issues pertaining to women's rights. These changes reflect the need for candidates to stay informed about evolving legal frameworks and socio-legal issues. This up-to-date knowledge is crucial for effectively answering questions related to law and its impact on society during the examinations.