The isochron technique of radiometric dating is often presented as overcoming problems with earlier methods. However, it is easy to imagine scenarios that could cause isochrons to yield false daates, and geologists recognize that isochrons can yield bad dates.

The idea of isochrons is this: Suppose X is a parent element that decays in to Y and Z is another isotope of Y not produced by radioactive decay. Let x, y, and z refer to their concentrations. Since Y and Z are isotopes, we would assume they have similar chemical properties. Let's assume that initially, the ratio of y and z is constant, and then X begins decaying to Y. We have two sources of Y, so y = c1 * x + c2 * z at the end of some time period. It follows that the ratios x/z and y/z have a linear relationship whose slope yields the age of the sample. If these ratios are observed to obey such a linear relationship in a series of rocks, then an age can be computed from them.

However, we can imagine situations in which such a linear relationship could be produced without indicating a true age. Let A and B be two rocks containing only X and Y and no Z. Suppose A is very old (or appears very old) and B is very young. Suppose A and B become thoroughly mixed. Their perceived radiometric age would then be between that of A and B. Now, suppose a mixture of Y and Z penetrates this mixture of A and B, in some places more than in others, but with a constant ratio of Y and Z. This will then yield a beautiful isochron, but the age given will be meaningless. This can also happen if water removes a constant fraction of X but no Y from A, making A appear older, and then the mixture of Y and Z enters. Another possibility is for A to have a constant concentration of X and Y at the beginning, and for more Y to enter, making A appear older. Then if a mixture of Y and Z enters, a nice isochron yielding a false age will be produced. A final possibility is for A to have a constant ratio of X and Y at the beginning. Then a lot more Y enters by diffusion. Then the rock is heated and mixed so the ratio of X and Y is everywhere the same. This makes the rock look much older. Finally, a mixture of Y and Z enters, different amounts at different places. This will also produce a false, and much too old, isochron. I would say that these scenarios are not at all implausible, especially when one considers that the daughter element Y is often argon, a gas that is relatively mobile in rock.

For a much more detailed discussion of isochrons and a variety of possible problems with them, and how geologists attempt to solve them, see http://www.talkorigins.org/faqs/isochron-dating.html.