We will deal with carbon dating first and then with the other dating methods.Carbon has unique properties that are essential for life on Earth.
After study and discussion of this question, I now believe that the claimed accuracy of radiometric dating methods is a result of a great misunderstanding of the data, and that the various methods hardly ever agree with each other, and often do not agree with the assumed ages of the rocks in which they are found.
Other radiometric dating methods such as potassium-argon or rubidium-strontium are used for such purposes by those who believe that the earth is billions of years old.
Radiocarbon is not suitable for this purpose because it is only applicable: a) on a time scale of thousands of years and b) to remains of once-living organisms (with minor exceptions, from which rocks are excluded).
The field of radiocarbon dating has become a technical one far removed from the naive simplicity which characterized its initial introduction by Libby in the late 1940's.
It is, therefore, not surprising that many misconceptions about what radiocarbon can or cannot do and what it has or has not shown are prevalent among creationists and evolutionists - lay people as well as scientists not directly involved in this field.