I think it's widely understood that questions should have a certain level of notability.
However, I also think that asking for references if you are unsure that the claim is actually a real notable claim is something the community should do, as well as down voting irrelevant questions and voting to close.
The problem is not that there is bad quality content coming our way. That's going to happen more and more as we grow and appear in google searches more frequently (for example). The problem in my opinion is that not enough people are helping the moderators.
Down vote content which is not good. Questions AND answers. It is shameful that bad questions and answers have sometimes 10+ up votes. They should have -10 votes.
Vote to close stuff which is off topic or actively bad for us.
Flag answers without references as not an answer. They are NOT answers. Each question has the hidden implied statement "I will only accept answers which are based on facts and experiment"
Ask for references in comments for questions and answers. Mods and 3/4 users shouldn't be the only ones doing it. There are 4000 users on this site and you only need 10 rep to comment.
For this site to work and scale with size, everybody has to do that. Moderators should be only handling edge cases, not doing the bulk of content sorting because not enough users help.
It's not a random choice that you have a review page and a tools page available. Use them. Help us moderate massively and make this site scale up with size!