Such failures may be due to laboratory errors (mistakes happen), unrecognized geologic factors (nature sometimes fools us), or misapplication of the techniques (no one is perfect).
We scientists who measure isotope ages do not rely entirely on the error estimates and the self-checking features of age diagnostic diagrams to evaluate the accuracy of radiometric ages.
Other objections raised by creationists are addressed in [Dalrymple2006a].
The overall reliability of radiometric dating was addressed in some detail in a recent book by Brent Dalrymple, a premier expert in the field. 80-81]: These methods provide valid age data in most instances, although there is a small percentage of instances in which even these generally reliable methods yield incorrect results.
Also, as the authors of the 1968 article were careful to explain, xenoliths cannot be dated by the K-Ar method because of excess argon in bubbles trapped inside [Dalrymple2006].
Thus in this case, as in many others that have been raised by skeptics of old-earth geology, the "anomaly" is more imaginary than real.
The simplest means is to repeat the analytical measurements in order to check for laboratory errors.Several hundred laboratories around the world are active in radiometric dating.Their results consistently agree with an old Earth.The latest high-tech equipment permits reliable results to be obtained even with microscopic samples.Radiometric dating is self-checking, because the data (after certain preliminary calculations are made) are fitted to a straight line (an "isochron") by means of standard linear regression methods of statistics.