LukeProg considers philosophy a diseased discipline. Firstly, he points out that continental and postmodern philosophy generally fail at being clear or rigourous. The problem with this objection, is that all groups have subgroups that are kind of crazy. Even the Rationalsphere has the reactionaries. That said, I would disagree with the notion that all continental philosophy lacks value. Some of Nietzsche's and Schopenhauer's ideas are very interesting. There is a lot of unnecessarily complicated continental philosophy with very little substance, so I would agree with mainly focusing on analytical philosophy, but I haven't really read enough continental philosophy to comment on the proportion of interesting content to pointless dribble. I also agree that philosophy spends too much time looking back into the past; while some basic knowledge of the history of philosophy is important and history of philosophy of subjects should be available for those who are interested in it, philosophy should focus on the most convincing material for the most interesting and contentious questions.
That said, there is still a lot of value in the study of philosophy. A good first year philosophy course will provide students with an introduction to utilitarianism (through the trolley problem), libertarianism, the free-will debate, materialism vs dualism, Hume's Is-Ought distinction, Hume's critique of induction, Descartes radical skepticism (which is valuable until he tries to use the ontological argument), Occam's razor, Karl Popper's criterion of falsifiability, Rawl's original position, the Ship of Theseus, the Socratic method, stoicism (valuable in moderation) and Epicurius (his egoistic theory of philosophy is quite bad, but some of his thoughts on how to live a happy life are quite interesting). There will also be discussion of moral relativism, including critiques which should hopefully help some students see why complete, normative moral relativism is very philosophically unsatisfying. Contrarily to LukeProg, knowledge of the Gettier Problem improves one's epistemology because it shows that knowledge equals justified true belief is not a viable stance.
Unlike Less Wrong, the philosophers who run philosophy courses have to be able to argue that their courses are non-ideological, so it is necessary for them to include material that they may perceive to flawed, but which was important either historically or in the contemporary debate. I think that there are benefits of having discussion of arguments that seem (and actually are) ludicrous, such as Berkeley's Immaterialism as it trains students to consider ridiculous sounding ideas and argue against them with logic instead of dismissing them out of hand. Philosophy also trains other skills, such as learning to state arguments precisely and questioning why we believe what we believe. Having to write down your views, whilst knowing that your reasoning will be critiqued
Many beginning philosophy students are not very good at focusing on a question and will often try to dodge hypotheticals. For example, when it comes to the trolley problem, they will bring up pragmatic concerns (such as will the fat man actually stop the trolley?) instead of engaging with the core question being asked. Skilled professors or tutors are really effective at moving student's back to the core problem and I assume that after a while a reasonable percentage learn to stop focusing on periphery matters.
I believe that studying philosophy can greatly enhance student's rationality. It doesn't cause all students to converge on a single, correct belief system, but I think this is expecting a bit too much. Reading Less Wrong doesn't accomplish this either, but I would suspect that the readers of Less Wrong would tend to be a much narrower group than those who take a philosophy course in college. The readers of Less Wrong tend to already possess a reasonable amount of rationality, so even though a philosophy course may not make someone rational by our standards, it may still have significantly improved their thinking.
I will admit that I took a third year metaphysics course after reading Less Wrong and I gained very little from it because the answers to most of the questions seemed very obvious after reading The Map is Not the Territory. I also did a philosophy of language course. Again, most of the problems discussed seemed kind of obvious, but I think I learned quite a bit from the examples discussed, the framing and simply from being asked to consider some of the questions.