Legally speaking, and depending on where you live, lawyer-client and doctor-patient relationships have defined limits, and so should "keeping your mouth shut". For example, if I accidently discovered plans, documents, or other communications that would otherwise be in violation of the law, or indicate conspiracy to violate the law. I would speak up. If I could help spare someones pain and suffering, I would speak up.
You always need to look at the risk vs reward aspect when determing whether or not you should pay attention or stick your head in the dirt. If the potential consequences are high, but reward is little, then stick your head in the dirt. If the consequences are low, but the reward is high, then I would pay attention.
The hard part for you, is determining what really matters to you and what risks are unnaceptable. And this is also highly dependant on what normative ethical system you subscribe to.