Most of the sources that attempt to attack methods ... drivel on about the wide range of factors that can introduce errors into these measurements, and they are quite right, there ARE factors that can introduce errors. They ignore two crucial points though - it's possible to cross check a sample using several different types of dating to see if they agree and act as a form of calibration, and also the scientists doing the dating are quite aware of the sorts of error factors that can affect the result and try to account for them when they can. Even the worst errors are not bad enough to push the age range down to 1000 years.
Specialization => understand the theory, applicable methods, their limits => correct for error. Thermal hit the nail on the head. That is why it works [and requires an advanced degree].
The idea of parent nuclei decaying is pretty straightforward for probably just about everyone here, but some the nuances require more depth. Anyway...
Below is a link that explains most of the details of radiometric dating. It takes the format of some creationist saying that some aspect of radiometric dating is false, followed by a scientist who proceeds to refute that claim. Obviously some bias, but still helpful in clearing up misconceptions nonetheless. In my experience only creationists, and more recently people who have a beef against Climate Change bring this sort of thing up, so naturally geologists address their specific concerns 99pct of the time. As a heads up, there is a fair amount of material and topics covered, so it's not the quickest read. Also, plenty of references in case anyone finds a specific topic worth investigating.
http://www.tim-thompson.com/radiometric.htmlObviously learning something that is incorrect in the first place, or misunderstanding the material, is much more harmful than being completely ignorant. Which seems to be the case with the arguments against this sort of thing. Understanding the limits and grey area of a field is just as important. Something can still be poorly understood but act predictably, therefore not damning the entire theory behind it. That's why we do research -- to understand every last knowable detail about everything! In case that sounds preachy, my apologies.