Update: Heinrich Paes from Alabama has made the following remark on Not Even Wrong: ...we proposed a spectacular solution to the LSND anomaly involving neutrino shortcuts in extra dimensions, published in Phys.Rev.D72:095017,2005 [hep-ph/0504096]. If you look at Fig. 5 in this paper, you will see that for a choice of the resonant energy in the region 200-300 MeV we not only predicted the small counting rate for electron neutrino events above 475 MeV, but also the large rates in the 300-475 MeV region! While the anomalous effect seen by miniBooNE might have a conventional explanation, it might well be the first hint for extra dimensions of spacetime!
Observe that in our interpretation the extra dimensions would not be 'spacetime', but rather further levels of quantization. It will be interesting to look at this idea further. Here is Matti Pitkanen's post on the matter. Matti points out that there is every reason to expect that MiniBooNE is consistent with LSND, because the latter operated at < 200 MeV which is in the realm of the low E anomalies just observed.