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As we stand now, the Higgs observation has confirmed the Standard Model. Knowing that the Higgs is real means we are on the right track and that we don't have to throw out work that has built on the mechanism over the last 40 years.
The problem is that we know the Standard Model is 'wrong'.. actually, a better word is incomplete, for example it doesn't include gravity, dark matter or dark energy. To help guide theorists to move 'beyond the Standard Model' and build a more complete model of the universe we need the LHC to find something new.
Other than these glaring omissions from the Standard Model, it is hard to find experiments that directly disagree with predictions made by the model. The paradigm for finding 'new' physics over the last century has been to smash things together harder and harder. I think most physicists have given up seeing direct evidence of supersymmetry at this energy, and so will have to wait for the LHC upgrade (doubling the energy).
What we can hope is that the Higgs being observed is actually not quite what the Standard Model predicts. It could be that the Higgs decays differently than expected, for example it may produce more photons.
This would be a very important hint of physics beyond the Standard Model. So from here, the work is only beginning (again)!
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