MiHsC (quantised inertia) gives an explanation for the galaxy rotation problem and cosmic acceleration, but other proposals like dark matter are flexible enough that they can also explain these observations. What is needed is a controlled laboratory experiment that can test MiHsC with no ambiguity.
The consequence of MiHsC is that if any object accelerates, then the inertial mass of all nearby objects increases slightly. One experiment that involved a huge change in acceleration was that of Podkletnov et al. (1992). They cooled a super-conducting disc (so there was little thermal acceleration) and then suddenly rotated and vibrated it (high acceleration). Sure enough, nearby objects appeared to lose weight, just as if they had gained a bit of inertia and were less sensitive to gravity (specifically objects above the disc). In some ways this is a good test of MiHsC since the change in acceleration is so large that the MiHsC effect is more easily detectable. The disadvantage is that this experiment is hard to reproduce since the half-superconducting disc is difficult to make.
Another experiment was done by Tajmar et al. (2009) who noted nearby horizontal (not vertical) acceleration anomalies in laser gyroscopes close to a spinning supercooled Teflon ring. This anomaly is exactly predicted by MiHsC, but the disadvantage of this experiment is that the disc accelerations are small so the effects are difficult to detect and reproduce, and the accelerometers (laser gyroscopes) needed are more complex than simply measuring weight.
A better experiment would include a bit of both and would go as follows: 1) cool a Teflon disc down to 5K in a cryostat (Teflon survives low temperatures), 2) suspend a test mass (say 30g) over the disc's edge (to get maximum mutual acceleration) from a pivoted cross bar, and suspend another mass from the other end onto a precision balance (with milligram sensitivity), 3) spin the disc as fast as possible and monitor the weight of the test mass. MiHsC predicts that for a disc with a radius of 5 cm and spun at, for example, 10,000 rpm and 30,000 rpm, the test mass will gain inertial mass and appear to lose 0.017% (5.1 mg) and 0.16% (48 mg) of its weight respectively (see eq. 11 of McCulloch, 2011). Maybe in 2014 a test can be done.. Happy New Year!
McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002. Preprint