1. You put grad students in the title. But you only mention natural sciences and mathematics in the text. What about social science? What about the humanities? I am a physicist but I would personally like to know about progress on major problems in all academic fields. If you limit yourself to only some disciplines how will draw the line and why? HN has the line "interesting to hackers", which makes it very very broad. It relies on undemocratic voting, and occasionally moderation, to separate the good from the bad.
2. The reason the quality of arguments at HN is relatively high, is primarily the software behind the HN scores system. It very effectively kills of many techniques that are used by people to raise their scores. Arguably, getting on HN front page is directly correlated to the visits/money you get, while on an academic forum people will only care for egoistical reasons. The problem will be less, but it will still exist. If the community takes on and starts to grow, it will need access to the HN points software which is not public at the moment as far as I know.
3. Discussion surrounding links to papers, news articles or essays are generally serious and 'valuable'. This is what HN does primarily. You are proposing a forum where people can talk about their own thoughts and ideas. There are many such internet forums for this purpose. Most of them degenerate into homework problem threads and how to get into grad school questions. Why? Because what you thought over breakfast this morning is usually not brilliant enough, while a paper/essay/news has had many hours of professional thought behind it.
4. It might be possible to piggyback over HN. Any link on HN relating to grad students can be manually resubmitted on the community website. The discussion happens on HN. The community website only serves as a curated list. This will solve the problem of drowning in the noise of software. Of course, the limitation will be that all posts submitted will have to conform to the "interest to hackers" criteria.