I find that a lot of questions in my tagged sets have been closed (normally without answer due to quality issues) - can these be either tagged so the can be filtered, or have some form of core filtering available?
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Ignoring broken windows is a bad idea -- it's important that the community see
Both of these things are critically important and neither can happen if we hide the "dirty laundry".
Now, if more than 50% of the questions on the home page are closed, then a site has much deeper problems of scope topic and messaging -- but there is no evidence this is the case.