In short, carbon dating is as useful as any other technique, so long as it's done properly and the results are objectively interpreted. How does young earth creationism view the fossil record? Is there a contradiction between faith in God and science?
It is not, however, an inherently error-free or black-and-white method for dating objects. Are the similarities in human DNA and chimp DNA evidence of evolution?
Multiple tests, and various testing, must be done to arrive at plausible results.
Also common is problematic results being thrown out because they are inconsistent with expected results.
Carbon dating, or radiocarbon dating, can be helpful in determining the relative age of an object, but has many limitations.
The testing for carbon dating relies on many factors and should be used in conjunction with other methods of dating materials.
Complicating things further, the Earth's concentration of carbon-14 changes based on a variety of factors.
As with any scientific testing, contamination can drastically impact the results of tests. Inconsistent results are often discarded under the claim of contamination.
Techniques include tree rings in timbers, radiocarbon dating of wood or bones, and trapped-charge dating methods such as thermoluminescence dating of glazed ceramics.
Coins found in excavations may have their production date written on them, or there may be written records describing the coin and when it was used, allowing the site to be associated with a particular calendar year.
This is not necessarily unusual in science, but one must keep in mind how assumptions and interpretations are related.