Here is a summary of most of the anomalies that have helped me in formulating and testing MiHsC. Although I do pay serious attention to all of them, I am not saying necessarily that all of them are correct, but I think taken together they do point the way to new physics. This new physics shows up at low accelerations (and so is unlikely to be seen in particle accelerators, where high accelerations are the rule). They are, in order of scale from the cosmic scale downwards:
The low-l cosmic microwave background (CMB) anomaly. This is radiation coming from all parts of the sky and the Planck satellite has shown that its variability on the largest scales is significantly lower than it should be. MiHsC predicts this: its Hubble-scale Casimir effect predicts that larger waves (ie: patterns) are suppressed because they don't fit within the Hubble scale (paper submitted).
It has been shown that the expansion of the cosmos is accelerating at a rate of about c^2/Theta where c is the speed of light and Theta is the Hubble diameter. Dark energy has been arbitrarily invented to explain this, but this acceleration is close to the minimum acceleration predicted by MiHsC, since any object with a lower acceleration would have its inertia made from Unruh waves longer than the Hubble-scale, and they would be unobservable (Mach's principle says they would not exist), so the object loses inertia and accelerates again (see paper).
Stars in galaxies orbit so fast that inertial forces should rip the galaxies apart. This does not seem to happen, so dark matter is added arbitrarily to hold them in, but it has been neither detected nor explained. MoND predicts this anomalous rotation, but needs a fitting parameter to do it, and doesn't work for galaxy clusters. MiHsC predicts the observed galaxy rotation and the behaviour of galaxy clusters without dark matter and without adjustable parameters by reducing the inertial mass of the low acceleration stars at the galaxies' edge (see paper).
Globular clusters within galaxies also show aberrant rotation when their internal accelerations fall below 2x10^-10 m/s^2. This cannot be explained by dark matter since it must be uniform at these scales to fit galaxy rotation. It can't be explained by MoND either since this depends on the total acceleration of the system, which is still large for these systems. MiHsC can potentially explain it (I haven't calculated this yet) since inertia in MiHsC depends on internal (local) accelerations.
The Pioneer 10 and 11 probes show an unexplained acceleration towards the Sun of about 8.7x10^-10 m/s^2. This has been modelled mundanely as a thermal recoil caused by radiation from the RTGs bouncing off the spacecrafts' radio dish, but this explanation needs a model with over 2000 finite elements and two adjustable parameters, whose details have not been published. The scope for errors is huge there. MiHsC predicts this acceleration far more simply as a loss of inertial mass that causes the spacecraft to respond more to the attraction of the Sun (see paper).
Spacecraft occasionally use the Earth in gravity assists and their flyby trajectories are carefully monitored. When they approach at a low latitude and leave at a high latitude they seem to gain an anomalous few mm/s in speed. MiHsC predicts something similar that is the right order of magnitude (see paper, but note I should have used the geocentric speeds for the spacecraft so the predictions of the anomalies are likely to be smaller). For tomorrow's Juno flyby (on 9th Oct, 2013) MiHsC predicts an anomalous 0.75 mm/s speed up.
Martin Tajmar and coworkers put rings of various materials in a cryostat (low thermal accelerations), spun the rings and found that accelerometers not in frictional contact with the rings followed their rotation, by a ratio of 3x10^-8 for clockwise rotations and half that for anticlockwise rotations. MiHsC predicts this behaviour exactly, since the sudden acceleration of the ring increases the inertia of the accelerometer and to conserve momentum it has to move with the ring. MiHsC even predicts the parity violation as being due to the rotation of the Earth with respect to the fixed stars (see paper).
Podkletnov and coworkers put a superconducting disc in a cryostat (low thermal acceleration), levitated it, and applied high frequency magnetic fields to make it vibrate (an acceleration of about 10^5 m/s^2). They detected a 0.06 percent weight loss in objects over the disc (more if the disc was rotated). MiHsC predicts that the sudden acceleration of the disc increases the inertia of the objects above, and makes them less sensitive to gravity: it predicts half the weight loss seen (see paper).
The fundamental phenomenon of inertia. This tendency of objects to keep going at constant speed has never been explained, and only a tiny part (0.1 percent) of it is explained by the Higgs field. I have shown that inertia can be explained (eg: the Planck mass to within 26 percent) by an 'asymmetric Casimir effect': when an object accelerates, say to the right, a Rindler horizon forms to its left and suppresses the Unruh radiation on that side causing a net force backwards against its acceleration. This is the first time inertia has been explained mechanistically, and without any adjustable parameters (see paper). It is the modification of this basic inertia by MiHsC (by the Hubble horizon) that predicts galaxy rotation & cosmic acceleration without dark matter or dark energy.
There are other anomalous observations or experiments that intrigue me but are not conclusive yet, the anisotropy of the CMB, the Bullet cluster, intergalactic alignments, galactic jets, pulsar jets, the Allais effect, extreme spin experiments, the variation of decay rates with Solar rotation, extreme energy cosmic rays, the peculiarity of the neutrino... If you know of any others, please let me know.