The particular example you bring up is one of the most famous such cases.The claims are really quite spectacular, when taken at face value, and therefore should be examined thoroughly.And the result of this accepted method dates dinosaur fossils to around 68 million years old. Its half-life ($t_$) is only 5,730 years—that is, every 5,730 years, half of it decays away.The theoretical limit for C-14 dating is 100,000 years using AMS, but for practical purposes it is 45,000 to 55,000 years.Such contamination would, however, reduce the apparent age of a 60,000-year-old object by almost 50 percent.
Contamination of this kind amounting to 1 percent of the carbon in a sample 25,000 years old would make it appear to be about 1,500 years younger than its actual age.Robert Kalin senior research specialist at the University of Arizona’s radiocarbon dating laboratory, performed a standard independent analysis of the specimens submitted by Hugh Miller and concluded that the samples identified as “bones” did not contain any collagen. These results corroborated established paleontological theories that assert that these fossiles presumably were 'washed away' over long periods of time by ground water, replacing the original bones with other substances such as the minerals naturally present in the water, implying that this sample could ).At this point, it is quite clear that there is little reason to trust the research by Miller's research group.If dinosaur bones are 65 million years old, there should not be one atom of C-14 left in them.Dinosaurs are not dated with Carbon-14, yet some researchers have claimed that there is still Carbon-14 in the bones. Do these data indicate that a more accurate method needs to be derived?
Furthermore, it appears less than certain that the carbon found in the bones actually had anything to do with them being dinosaur bones.