I remember getting into a debate with a (facebook) acquaintance of mine, ultimately it boiled down to me asking them for an example of what they'd consider a good sociology paper. The paper was trying to test whether sexual harassment training actually worked. After reading through it, it was almost laughable how bad it was. Their system for measuring if the training worked was waiting two weeks and testing if people retained the knowledge. It was also done using a small group of college students.
Of course that's just one paper, but the event stuck in my mind. He was a relatively well-respected grad student in my peer group, and that was what he considered to be good science?
There are a lot of examples of really dubious stuff coming out of the academic community. Things like the sokal affair, or the infamous "feminist glaciology" incident. Like it or not those are getting lumped in with legitimate scientists in the public conscious, and if academia want to get taken more seriously it needs to get these ridiculous excesses under control or at least de-emphasize/disavow them as much as possible.
I think there's a lot to be done to gain back that trust, but most of it has to do with cutting out the garbage. Publish or perish seems like one of the bigger problems that need addressing, but the lack of open-access journals certainly doesn't help. The academic writing style probably needs an overhaul as well.
I don't know, it's sad but for me at least there needs to be some big changes before I start regaining respect of academia as a institution.