Utilizing jstack for debugging live Java production servers offers the advantage of obtaining stack traces of all Java threads, helping identify performance bottlenecks and stuck threads without adding performance overhead. However, it has limitations, such as not providing variable states and requiring manual activation during issues. To enhance its utility, the text suggests techniques like creating stateful thread data by setting meaningful thread names to provide context and parameters, and automating jstack activation for continuous monitoring by invoking it programmatically under certain conditions. This approach allows developers to capture necessary data without impacting the application's stability while ensuring detailed logging for troubleshooting.