A product manager's level of technical knowledge can vary depending on the specific role and product they are working on. While some may require a deep understanding of software engineering, others may be sufficient with just a basic understanding of technology. Having technical knowledge as a product manager can inform better decision making, enable better communication with the technical team, and help understand the market. It is also essential for prioritizing bugs effectively and balancing time and resources spent fixing them with overall product goals. To improve their technical knowledge, product managers can take courses such as Harvard's CS50x course, CodeAcademy, Udemy, or Coursera, build their own products, and continuously learn through experience and mentorship from technical experts.