Large Language Models (LLMs) have gained significant attention in the medical domain for their human-level capabilities, leading to increased efforts to explore their potential in various healthcare applications. However, despite such a promising future, there are multiple challenges and obstacles that remain for their real-world uses in practical settings. This work discusses key challenges for LLMs in medical applications from four unique aspects: operational vulnerabilities, ethical and social considerations, performance and assessment difficulties, and legal and regulatory compliance. Addressing these challenges is crucial for leveraging LLMs to their full potential and ensuring their responsible integration into healthcare.