How can we definitively tell if the vacuum over there has the same energy density as the vacuum over here?
This comes from measurement of the fine structure constant. The virtual particles created as a result of the vacuum energy interact with electrons, causing small changes in the elementary change of the electron, and int he electromagnetic coupling between charged particles. This effect is accounted for in QED, and has been observed in the spectra of Hydrogen as difference in the energy levels of 2S1/2 and 2P1/2 orbitals (http://en.wikipedia.org/wiki/Lamb_shift). Measurement of the fine structure constant from atomic spectra allows us to measure if the elementary electric charge has changed over time or at different locations in the universe, essentially a remote measurement of the uniformity of vacuum energy.
Some measurements do suggest that the fine structure constant has changed over time, or that it isn't uniform throughout space over galactic scales. Indeed, there is no reason why it should be. That said, I would be surprised if the inhomogeneity is balanced by the accelerating expansion rate of the universe. Hence the problem of apparent increase in energy and violation of conservation of energy.