The differences actually found in the scientific literature are usually close to the margin of error, usually a few percent, not orders of magnitude!
Vast amounts of data overwhelmingly favor an old Earth.
Other objections raised by creationists are addressed in [Dalrymple2006a].
Another method is to make age measurements on several samples from the same rock unit.
This technique helps identify post-formation geologic disturbances because different minerals respond differently to heating and chemical changes.
The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
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).