Key assumptions are generally tacit (which is to say, nonexplicit) assumptions that underlie a causal model and are essential to that causal model making good predictions. Research work by CIA analysts indicated that key assumptions had a base rate of turning out to be wrong 25% of the time. As most models contain several key assumptions, we begin to see why having multiple working hypotheses and having plans be robust to model uncertainty plays such a big role in accurate prediction.
Some examples of prompts that help generate potential key assumptions are the so called journalist questions: who, what, where, why, how, and when? As well as generating 'absolute' statements about the model, using words such as always, never, can't, must, all, none, etc.