The following is taken from an unpublished manuscript of mine:

Most recent alternative cosmologies [71, 72, 73] also propose explanations for the Pioneer anomaly [74, 75], an apparent unexplained acceleration of about 8.7 10^-10 m/s² directed towards the Sun, observed in the trajectories of space probes. These alleged explanations are no good sign, since the anomaly can be traced back to an evident modification in the acquired tracking data that was introduced on January 1st, 1990. This can be seen in an analysis of publicly accessible data [76]. It shows that there was no anomaly in the data from Pioneer 10 before that date, when it suddenly appeared very clearly and remained. Despite extensive and inconclusive investigation of a range of imaginable causes of the anomaly by the Jet Propulsion Laboratory, this modification goes unmentioned in the papers published by the group. Since the apparent mistake (perhaps GR related) is likely to have been committed also in the tracking of other space probes and perhaps in a wider range of astronomical calculations, it would be appropriate to clarify its origin, nature and spread, and to correct for it.¹

Footnote:
¹ In [75] one can read: ”One can demonstrate that beyond 15 AU the difference between the predictions of Newton and Einstein are negligible”. This is said without any warning that it holds only for observations made from a still larger distance from the Sun but not for those made from Earth. This evokes a suspicion that the Pioneer anomaly may have arisen from a similar but less drastic inadvertence.

References:
71. Masreliez, C.J.: Scale expanding cosmos theory I –An introduction. Apeiron 11, 99-133 (2004)
72. Crawford, D.F.: Observational evidence favors a static universe (Part I) Journal of Cosmology, 13, 3875-3946. arXiv:1009.0953 (2011)
73. Brynjolfsson, A.: Plasma redshift shows that there is no anomalous acceleration of Pioneer 10 and 11. B. Am. Phys. Soc. 55, http://meetings.aps.org/link/BAPS.2010.NEF.B1.26 (2011)
74. Anderson, J.D., et al.: Study of the anomalous acceleration of Pioneer 10 and 11. Phys. Rev. D 65, 082004 (2002)
75. Turyshev, S.G, Toth V.T,: The Pioneer anomaly. Living Rev. Relativ. 13, 4-175 (2010).
76. Unzicker, A., Schmidle, D.: A quick and dirty approach to verify the Pioneer anomaly. (2007) http://arxiv.org/abs/gr-qc/0702151

See also: 
Eiermann, K.E.: The Pioneer anomaly and new physics. Astron. Nachr. 333, (2) 182-185 (2012). http://onlinelibrary.wiley.com/doi/10.1002/asna.201111641/abstract

Have a look at the graphs in ref. 76!

Very interesting, indeed!

I am still thinking that the relatively good agreement of the 8.7 10^(-10) m/s² with the product H_0 * c could have its reason in some kind of new physics.
Eiermann (2012) proposes such new physics (a variant of variable mass hypothesis (VMH) similar to the one of Arp and Narlikar).

I'm very interested in the general opinion of others about the VMH ideas!

Best wishes,
S.