The rapid digitalization of healthcare has led to an unprecedented reliance on software systems to improve patient care, streamline operations, and ensure regulatory compliance. This article presents a comprehensive analysis of the critical role that software engineering and quality assurance (QA) play in three key areas of modern healthcare: Electronic Health Records (EHRs), telemedicine platforms, and medical device software. Through an examination of current practices, challenges, and case studies, we demonstrate how robust software engineering methodologies and rigorous QA processes contribute to the development of reliable, secure, and efficient healthcare applications. Our findings highlight the importance of data integrity, interoperability, user experience, and regulatory compliance in healthcare software development. Furthermore, we explore emerging trends such as artificial intelligence, blockchain, and the Internet of Medical Things (IoMT), discussing their implications for future software engineering and QA practices in healthcare. This article provides valuable insights for healthcare organizations, software developers, and policymakers, offering recommendations to enhance the quality and safety of software-driven healthcare solutions.