Update, opening the observatory doesn't do anything bad if I open it immediately upon firing up the game. However, if I go to the tracking station or map view, and then the observatory, the game ends up in a bricked state of the KSC where I can look around but not click on anything.
EDIT: Okay, I've done some scrolling back and seen people having the same issue. Thing is, the culprit in those situations always seems to be entering the SOI of an undiscovered body. I have not done anything of the sort. In fact, I have only visited Kerbin, the Mün, and Minmus, all three of which I have configured to start discovered.