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Nope; gravity is very predictable and very constant (see also the difficulty in detecting gravitational waves), they calculated how much it should accelerate under influence of gravity and found the actual acceleration to be different.

As for the unexpected attraction, as one of the moon astronauts displayed, objects of different mass are attracted (fall) equally quickly by gravity in a vacuum.

Thanks for your comments, they have kicked me out of my head space. I suppose I got it into my head thinking of massive densities, like densities of neutron star. Anything dense enough to make a difference would be very loud and easy to spot... as I'm writing this, even if it were very dense. The effect would only be seen when it is much closer to another gravity well. Ok, how about this (I'm still stuck on this gravity idea), there is an unseen "cloud" of rock orbiting (very) slowly round the main body. Seemingly slowing down and accelerating as it orbits. A small body or cloud of bodies could easily be small enough for us to not see it, but enough to cause this effect. Sound reasonable?

Gravity doesn't work that way, I'm afraid, as Galileo demonstrated.