Clinical summarization is crucial in healthcare as it distills complex medical data into digestible information, enhancing patient understanding and care management. Large language models (LLMs) have shown significant potential in automating and improving the accuracy of such summarizations due to their advanced natural language understanding capabilities. These models are particularly applicable in the context of summarizing medical/clinical texts, where precise and concise information transfer is essential. In this paper, we investigate the effectiveness of open-source LLMs in extracting key events from discharge reports, including admission reasons, major in-hospital events, and critical follow-up actions. In addition, we also assess the prevalence of various types of hallucinations in the summaries produced by these models. Detecting hallucinations is vital as it directly influences the reliability of the information, potentially affecting patient care and treatment outcomes. We conduct comprehensive simulations to rigorously evaluate the performance of these models, further probing the accuracy and fidelity of the extracted content in clinical summarization. Our results reveal that while the LLMs (e.g., Qwen2.5 and DeepSeek-v2) perform quite well in capturing admission reasons and hospitalization events, they are generally less consistent when it comes to identifying follow-up recommendations, highlighting broader challenges in leveraging LLMs for comprehensive summarization.