The global mental health crisis is looming with a rapid increase in mental disorders, limited resources, and the social stigma of seeking treatment. As the field of artificial intelligence (AI) has witnessed significant advancements in recent years, large language models (LLMs) capable of understanding and generating human-like text may be used in supporting or providing psychological counseling. However, the application of LLMs in the mental health domain raises concerns regarding the accuracy, effectiveness, and reliability of the information provided. This paper investigates the major challenges associated with the development of LLMs for psychological counseling, including model hallucination, interpretability, bias, privacy, and clinical effectiveness. We explore potential solutions to these challenges that are practical and applicable to the current paradigm of AI. From our experience in developing and deploying LLMs for mental health, AI holds a great promise for improving mental health care, if we can carefully navigate and overcome pitfalls of LLMs.