> I could throw something on my roof or out my window that could somehow be part of a global network to watch things and making findings as a community.
In addition to the other items people have mentioned, the Center for Backyard Astrophysics is a network of small observatories (most operated by serious amateurs) that assembles light curves (brightness as a function of time) for various types of stars and stellar binaries. It's not a fully automated system, but presumably you could set up a robotically operated telescope to assist with their programs.