Nuclear testing and the Anthropocene, a chemostratigraphic link?
Certain anthropogenic radionuclides have pragmatic advantages as markers for the start of the anthropocene.  The advantage of radionuclides over anthropogenic stable nuclides is that the primordial production of all but a few radionuclides has decayed away.  Thus natural background levels are below detection by sensitive analytical methods except in a few localized situations (e.g. preCambrian natural reactors). Even radionuclides that occur naturally may be useful if the anthropogenic signal is much greater than the natural levels. 

An important trait for a radionuclide stratigraphic marker is that it has a long enough half-life so the anthropogenic material remains in the sediments.

The other important trait for a stratigraphic marker is that it is not redistributed significantly in the environment and stays with the sediments of the proper age. For this reason, 137Cs and plutonium isotopes are valuable since they have low solubility/strong adsorption onto sediments and were distributed widely by atmospheric nuclear testing. However, this does not mean that the radionuclides won't be redistributed. The radionuclides can be redistributed by water, wind, or mass wasting. Colloidal transport can move particles even in saturated groundwater and the vadose zone. In fact, levels of atmospheric fallout plutonium have been used to interpret the redistribution of other contaminants. 

Even with very low solubility there can be some dissolved transport into earlier or later sediments. For example, Woods Hole Oceanographic Institute has determined that plutonium mobility may be affected by oxidation state and that more mobile 244Cm can be transported before it decays to 240Pu. 

Thus, anthropogenic radionuclides, particularly those of long half life and low solubility that were produced during atmospheric testing, have properties that make for pretty good stratigraphic markers. But the limitations should be kept in mind.

An additional problem is in defining the 'start' of the anthropocene as fitting your marker rather than the other way around.  Certainly, people have had had geologic and ecological impacts before 1945. There are indications that aboriginal burning regimes over 20,000 years caused nutrient export with effects that can be seen in current groundwater chemistry.