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There seems to be a mundane explanation, according to a just published article in New Scientist.

Excerpt:

But now the verdict is that a substantial part of the anomaly, at least for Pioneer 11, is due to thermal effects, according to Slava Turyshev of NASA's Jet Propulsion Laboratory in Pasadena, California, US. He described his findings on 13 April at a meeting of the American Physical Society in St Louis, Missouri....

...Pioneer 11 gives off heat in certain directions more than others. The uneven heat emission is enough to nudge the spacecraft off course, accounting for 28% to 36% of the anomaly....Turyshev suspects that the optical properties of the spacecraft's exterior may have changed during the mission, possibly degrading due to dust hitting the craft and ultraviolet radiation from the sun.

That might make the spacecraft radiate more heat than expected. However, it's not clear yet whether these changes to the spacecraft's exterior could account entirely for its unexpected trajectory.

Besides, the scientists who have measured the Pioneer anomaly are smart enough to account for relativistic effects, such as changes in mass and the curvature of spacetime.

They don't need your "Mind of Man" suggestion that the speed of light (or its square) is not well measured. In fact, the value of c is known to a much greater precision (I'm guessing one part in 1012 or so.) than the anomaly, measured by the tools of better men and women than you or I.

Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)