Progress in astrophysics entails instabilities, some of which are beneficial in leading to unanticipated advances. Often these come about through the import of new tools developed in other sciences or for industry or the military. Other instabilities, however, can be harmful and lead to setbacks. The history of 20th century astronomy is replete with examples of both types, some of which I will recount. One source of instability is astronomy's inability, sometimes for decades at a time, to systematically pursue discoveries of rare events. Such delays inject levels of uncertainty in our observational discipline that the experimental sciences seldom encounter. Partial remedies for this difficulty may already be available. Other instabilities arise as the complexity of the various disciplines constituting our field increases, the tools and vocabularies used by the disciplines begin to diverge, and misunderstandings arise to threaten a coherent, unified view of the Universe. As historical examples show misinformation then cascades throughout astrophysics, with consequences akin to those of major failures of electrical power grids or financial meltdowns. I will outline ways to retain beneficial instabilities while more readily thwarting damaging intrusions.