Large Language Models (LLMs) are increasingly used in high-stakes domains like law and research, yet their inconsistencies and response instability raise concerns about trustworthiness. This study evaluates six leading LLMs—GPT-3.5, GPT-4, Claude, Gemini, Mistral, and LLaMA 2—on rationality, stability, and ethical fairness through reasoning tests, legal challenges, and bias-sensitive scenarios. Results reveal significant inconsistencies, highlighting trade-offs between model scale, architecture, and logical coherence. These findings underscore the risks of deploying LLMs in legal and policy settings, emphasizing the need for AI systems that prioritize transparency, fairness, and ethical robustness.