Honestly, I find the "searching" status confusing myself... It used to correspond to actual searching, so I guess that some of the connections are still left to give feedback.
As for the stable version having bugs, it does, but IIRC it didn't have
known (new ones ; bugs already in the previous stable and still unfixed are no reason not to release) bugs when it was released. Having few testers for the debug builds unfortunately means that most bugs are not found until stable release happens and more users start using it. Lots of complaining about stupid developers then follows.
I've been using debugs for a while myself and the quality is variable. A build right after a new feature was added might crash on start. A build right after lots of bugs were fixed might be more stable than the "stable" release you get from the web site... My advice would be (from my personal experience, YMMV): go debug, but be prepared to go back to a previous build and don't feel compelled to keep up-to-date with builds if the current one is working and you are not in the mood to deal with weird problems right now. I usually only update every month or two since most improvements are to things I don't use. But the debug has lots of bug fixes for problems in the "stable" build... So going from the stable to debug might be worth it.