Once upon a time in a lecture I attended, the lecturer had clearly not fully understood the material and was struggling to explain it. I was a student, but very knowledgeable about the topic, and had taught it many times in informal settings, so I felt silly just listening.
In the interest of the other attendees' learning, I considered offering to take over the lecture. However, I stopped myself, out of concern that the lecturer might feel humiliated, or think I'm questioning their authority more generally.
In such a situation, is it appropriate for a student to offer to teach a topic? What about other teaching staff who are attending? How would one politely suggest it, or otherwise deal with the situation?
Related questions: From a student's perspective: offering alternative viewpoints on lecture content, handling unintelligible lecturers and handling lecturers who just read from the book. From a lecturer's perspective: teaching a class you've never taken.