What power do student councils typically hold? And what role do they have? So, awhile back I wrote this answer suggesting that the student council would be ideal to handle the issue, but got told that student councils have no influence/role in such matters. In general I am used to the idea that a student council and student representatives do anything where students have to be represented at a higher level (from specific studies, to the faculty level, to the university level, up to even international politics). This does not only mean being a part of the rule making process, but also making sure students aren't disadvantaged because of professors not following those rules. Now, today I came across this question and a comment (+22) on the highest voted answer warns the OP against escalation, because of retaliations against him as a student. For me that's exactly the kind of thing where I would expect the student representative to step in, he would first approach the professor in his role as student representative (not revealing the names of individual students). If the professor doesn't resolve the issue at once the student representative would know - unlike a typical students - exactly who best to approach within the institution and is best aware of all the rules and systems that are in place (and importantly if a dean for example were to ignore student complains too many times a student council is able to escalate this easily to upper university levels).

Now, it's becoming clear to me that that's not how it works in a lot of institutions as a lot of answers which I would expect to be "go to your student representative" are instead complex diplomatic answers or just "live with it" answers, so what I am trying to understand is where this model does apply (is it typical of just some western countries? Europe in general? Only our institution?). And how a student councils activities and responsibilities broadly look in different systems.
Austria is in a rather interesting situation regarding this. Traditionally, Austrian universities were mandated to maintain what was called (roughly translated) "university democracy", meaning that all members of the university (students, non-faculty scientific employees, non-scientific employees, faculty) need to be able strongly influence all decisions that directly impact them. In practice, this led to (for instance) student representatives with quite real powers, such as vetoing certain decisions.

After 2002, a new legisation was put in place to "americanize" the system, which (interestingly) was also understood to mean that decision power should be centralized more or less purely in the faculty (in Austria that's basically only full professors). Since then, the role of student representatives has shrunk perpetually. They are still in most meetings, but if they disagree, the only consequence is a note in the meeting protocol. This has certainly led to some developments that were quite frankly not in the student's best interests.

That being said, in Austria, student representatives are still your best bet when you have some "systemic" problem with a lecture or a professor. Not necessarily because they have any power to change things, but at least they are on first-name basis with the people that do (the dean of studies, the responsible department head, etc.) due to sitting on many meetings with them. Even if they can't force anything, they should know who to talk to, who might be able to remedy the situation.