Here is a summary of further work on the time dilation experiment: from
https://www.physicsforums.com/threads/a-g-kelly-and-his-criticism-of-relativity.371910/"No. Certain internet kooks, including someone named A.G. Kelly, have produced reanalyses of the Hafele-Keating data[Hafele 1972] in an attempt to disprove relativity. This is just silly, because the experiment was reproduced four years later to much better precision,[Reisse 1976,Williams 1976] and again in a 25th-anniversary reenactment. The GPS system depends on general relativity, so any time you use a GPS receiver, you're reproducing relativistic time dilations of the type seen by Hafele and Keating.[Ashby 2003]
Hafele and Keating, "Around the world atomic clocks:predicted relativistic time gains," Science 177 (1972) 166.
Hafele and Keating, "Around the world atomic clocks:observed relativistic time gains". Science 177 (1972) 168.
R.A. Reisse, "The Effects of Gravitational Potential on Atomic Clocks as Observed With a Laser Pulse Time Transfer System," University of Maryland Ph.D. dissertation (May, 1976).
R.E. Williams, "A Direct Measurement of the Relativistic Effects of Gravitational Potential on the Rates of Atomic Clocks Flown in an Aircraft," University of Maryland Ph.D. dissertation (May, 1976).
C. Alley, "Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses," in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, Plenum Press, New York, 1983, ISBN 0-306-41354-X, pp. 363–427. This is available online and gives a summary of Reisse and Williams' dissertations.
Ashby, "Relativity in the Global Positioning System,"
http://www.livingreviews.org/lrr-2003-1 "
As is typical with scientific progress, an initial interesting experimental result is retried in later years with better equipment to see if it stands up.