Does Quantum Mechanics Allow Macroscopic Anomalies?

I've read a few other posts, and none seem to give me an answer that satisfies my curiosity. Thus far I've only been studying time independent QM, so I'm not even sure how wave functions evolve over time for microscopic things, let alone macroscopic things. However, what mandates that events that expect to happen actually happen? Why does it make sense that when I put something in a box, that it should remain in the box, rather than tunneling elsewhere? Or why should a pot ever come to a boil? Certainly these questions are being caused from a tragic misunderstanding of quantum theory, can someone clarify for me? At the end of the day, there is a nonzero probability that macroscopic anomalies will occur, right?