I clicked on the link you provided and found it made a few statements and then provided another link to a creationist website. This website has a short summary on carbon 14 and then referenced a number of papers that supposedly showed wild dates for carbon dating. But at least it has references to original articles. Note by the way that all the references on this page were dated from 1963 to 1984. Seriously, science has moved on a bit since then.
In any case, I accessed the article in question (Science vol. 224, 1984, pp. 58-61) to find that it was indeed a study looking at some problems with carbon dating, but instead of this being a negative as the creationist site wanted to push it as, the study provided a great deal of imformation about why inaccurate results might be obtained under certain conditions. In this case the erroneous results were attributed to fixation of dissolved hydrogen carbonate ions with which the shells are in carbon isotope equilibrium.
You see this is what scientists do, they not only work out methods that provide answers to scientific questions, but they also continue to work out the scope and limitations of the methods, what matrices, contaminants, or conditions can affect the results and how such issues can be identified and taken into account, so that they can be confident in the validity of test results.