Depending upon just what sort of 'inhomogeneity' you wish to probe, there are several observational programmes you could undertake.
For example, the 3D distribution of luminous baryonic matter - are there regions of the observable universe where galaxies, clusters, superclusters, walls, voids etc are distributed differently than in the rest of the observable universe? To some extent, the 2dF and SDSS surveys answer these questions, as does 2MASS (AFAIK, no inhomogeneity found).
The CMB can be used as another probe, both what we see from Earth, and the (past, distant) temperature we can infer from spectroscopic studies of distant gas clouds.
A different probe might be the 3D distribution of GRBs, assuming that one day we can measure their distance to within +/- 30% (say).
Finally, there is the in principle probe of the neutrino equivalent of the CRB. Sadly there appears to be no way we can even detect this, let alone use it to probe inhomogenities, without some major developments in particle physics.