Some critics, particularly religious fundamentalists, argue that neither fossils nor dating can be trusted, and that their interpretations are better.
Other critics, perhaps more familiar with the data, question certain aspects of the quality of the fossil record and of its dating.
Different methods have their own limitations, especially with regard to the age range they can measure and the substances they can date.
A common problem with any dating method is that a sample may be contaminated with older or younger material and give a false age.
Sedimentary rocks are rarely useful for dating because they are made up of bits of older rocks.