If I remember rightly, that's where poor old Popper came unstuck: having thought of the falsifiability criterion, he couldn't work out how to rigorously make it flexible. And as no experiment's exactly 100% uppercase-D Definitive, that led to some philosophers piling on the idea of falsifiability, as JoshuaZ said.

But more recent work in philosophy of science suggests a more sophisticated way to talk about how falsifiability can work in the real world.

The key idea is "severe testing", where a "severe test" is a test likely to expose a specific error in a model, if such an error is present. Those models that pass more, and more severe, tests can be regarded as more useful than those that don't. This approach also disarms the "auxiliary hypotheses" objection JoshuaZ paraphrased; one can just submit those hypotheses to severe testing too. (I wouldn't be surprised to find out that's roughly equivalent to the Bayes net approach SilasBarta mentioned.)