How would an eruption affect radiocarbon dating? Nuclear testing above ground and the burning of fossil fuels might affect the outcome of radiocarbon dating.
How would an eruption the size of Yellowstone or larger affect radiocarbon dating?
 A: The measurement of C-14 can be accurate. The interpretation of the measurement, in terms of the presumed age of the sample, is the thing that is subject to careful calibration.
The assumption of carbon dating is that the ratio of C12/C13/C14 in the sample had some known value at the time the organism was alive. "Known" does not mean "constant over all time", since there may be variations in the rate of C-14 production, and thus the amount of available C-14 in the biosphere at a given time.
Once the carbon atoms are incorporated in the tissue, and the tissue dies, it is assumed that the only thing that affects the ratio is the decay of the (slightly) unstable C-14. However, all kinds of contamination can bring other C-14 atoms into the sample and affect the measurement - making dating beyond a few 10's of 1000's of years an nearly impossible task, and putting at risk even more recent materials if improperly handled.
A very large eruption is likely to "stir the pot" - changing the C-14 composition significantly for a considerable period. Calibration is always necessary for any careful measurement - see for example this link for some notes on things like the change in the Earth's magnetic field and climate on the availability of C-14 (and calibration using tree rings, among other things).
