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The following is from Wikipedia on the anomilies of gravity. 

I don't claim to understand much of this, but I have been following the debate on the nature of Dark Matter and the expansion of the universe.

There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.

• Stars on the outskirts of galaxies are moving faster than they should. Also galaxies within galaxy clusters are moving faster than they should. Dark Matter and MOND have both been proposed as explanations.

• The expansion of the universe seems to be speeding up. Dark Energy has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data is reinterpreted to take this into account, the expansion is not speeding up after all.^[18]

• The Pioneer spacecraft seem to be slowing down in a way which has yet to be explained. ^[19]

• Various spacecraft have experienced greater accelerations during slingshot maneuvers than expected.

• An apparent frame dragging effect has been measured by Martin Tajmar and others which exceeds that predicted by General Relativity by many orders of magnitude.