I'm not aware of anything explained by OT that cannot be explained by rule-based phonology. The reasoning in OT is generally circular. A claim is made that there is a constraint of some sort in a certain language, it is argued that the constraint cannot be adequately described with rules of standard generative phonology, and the conclusion is drawn that this language has this constraint.
Let me review that. There is a constraint which is not describable in generative phonology, therefore this constraint exists. It may be interesting that rule-based phonology does not correctly account for everything, and it's good to know about such cases. Maybe we can find a better theory. But how does it follow that OT is a better theory? Or any theory at all?
It is a characteristic of scientific theories that they make predictions. When we find something that generative phonology can't handle, that tells that (1) generative phonology did make a prediction, and (2) it's not correct. When we find something that OT can't handle (if that is even possible), what do we do? We add a new type of constraint to OT and claim to have made a theoretical advance. Isn't that a little weird?
I am completely in sympathy with OT's contention that surface constraints are relevant to phonological structure and that this cannot be appropriately described in the original form of generative phonology. But this is not exactly news that was first brought to light in OT. Phonologists have been looking at such cases for a while -- for instance, there is Kiparsky's description of rule and rule-interactional transparency.
My own theory about transparency is that a theoretical constraint of the original generative phonology, the restriction of conditions on rule application to the inputs of phonological rules was incorrect, and not even well thought out. Generative phonology was supposed to be "neutral between speaker and hearer", so what sense did it ever make to restrict conditions on rule application to rule inputs?
I gave some detail about this in this forum in an earlier post on eliminating intermediate forms.