I think what would happen would depend on what exactly was discovered.
The result in general would be a search for a new theory which could explain both the newly discovered facts,
and the fact that the ToE has been, up to that point, so thoroughly successful. Every new theory has to explain the success of the old one: for example, the theory that the earth is a large sphere does account very well for the success of the theory that it was flat. Locally, it is flat to a good degree of approximation, and we should expect this to be the case if it was a sphere.
If I was you, I decide what the new theory would be, and then figure out from that what the anomaly would be. Otherwise, your novel will lack the sort of intellectual consistency necessary to good science fiction. Sure, one could overturn the theory that pigs can't fly by seeing lots of flying pigs, but a novel in which pigs suddenly started flying around would not really be science fiction unless there turned out to be a reason for it.
For example (this is probably not what you're looking for, though) suppose that billions of years ago aliens left a device on our planet --- let's call it a Speciator --- which makes new species. It does so on a trial and error basis, trying out new designs and then seeing how they do, and then trying out new (saltational) variations on those that did well. It would have to be mobile to avoid being destroyed or buried over all that time, and it would presumably have some sort of program for keeping itself hidden from observation by sapient beings such as ourselves. One day it starts malfunctioning, and starts generating a whole array of outmoded forms --- it starts churning out dinosaurs and pterodactyls. Following this disturbance to its epicenter, scientists discover the Speciator.
This would be consistent with observation, because up until the point where it started malfunctioning, it would in fact produce results in genetics, morphology, the fossil record,
et cetera, much like those that we ascribe to evolution.