1. DARK MATTER of an unknown form makes up most of the matter of the universe. This matter is not predicted by the standard physics models. The so-called "Theory of Everything" does not predict and does not understand what this substance is.
2. THE LAW OF GRAVITY appears to be seriously broken. Experiments by Saxl and Allais found that Foucault pendulums veer off in strange directions during solar eclipses. Interplanetary NASA satellites are showing persistent errors in trajectory. Neither of these is explained or predicted by the standard theory of gravity known as Einstein's General Relativity.
3. COLD FUSION. The Cold Fusion phenomenon violates physics as we understand it, and yet it has been duplicated in various forms in over 500 laboratories around the world. Studies by the Electric Power Research Institute, a large non-profit research organization funded by power companies, found that Cold Fusion works. A Navy study once also verified the reality of Cold Fusion, and the original MIT study which supposedly disproved Cold Fusion has been found to have doctored its data. Present day physics has no explanation for how it works, but it does work.
4. CHARGE CLUSTERS. Under certain conditions, billions of electrons can "stick together" in close proximity, despite the law of electromagnetism that like charges repel. Charge clusters are small, one millionth of a meter in diameter, and are composed of tens or hundreds of billions of electrons. They should fly apart at enormous speed, but they do not. This indicates that our laws of electromagnetism are missing something important.
5. COSMOLOGY. Quasars, which are supposed to be the most distant astronomical objects in the sky, are often found connected to nearby galaxies by jets of gas. This suggests that they may not be as far away as previously thought, and their red shifts are due to some other, more unusual physics which is not yet fully understood.
6. SPEED OF LIGHT,once thought unbreakable, has been exceeded in several recent experiments. Our notion of what is possible in terms of propagation speed has been changing as a result.