The process of radiological dating has several intrensic flaws, the most glaring of which is that it assumes set levels of the isotopes measured between samples origionally. For example, in U238 dating, the U238 decays into lead. The only problem with dating samples based on the ratio of the two is that lead occurs natrually, and often in the company of uranium and other heavy metals. The ratio of natural lead to uranium is not constant ether, as lead can occur with little or no radiological involvement. Basically, there is no way of predicting the actual decay time on the remaining U238, as extra natural lead is everywhere and probably with the uranium wherever it may manifest. This same inaccuracy is inherant in all other methods of radiological dating. Nothing says that the levels of carbon 14 are or were constant at any point in history, or that the levels of solar radiation that cause the isotope in the atmosphere were ever constant.
Radiometric dating using uranium/lead involves the analysis of zircon crystals. Zircon crystals readily incorporate uranium into their structure but do not do so with naturally present lead. The lead that is present in the structure of the zircon structure can thereby be assured to be radiogenic (decayed from uranium). Thus this is not as much a major issue that you present here.
Also, several radiological dating method have various different factors than can adversely influence the results. However scientists take this into account and place a error factor into these results. Their are also many work arounds with these as well as comparison analysis made with other dating methods. For example, if dozens of dating methods pointing to the old age of earth i.e. 4.5 billion years and a couple of dating methods have slightly different results (say 4 billion instead of 4.5 billion years for the age of a rock), this does not mean that we should throw out this estimated age and say that the Earth is really 6000 years old because people interpret an ancient manuscript to say so.