Has the Earth been exposed to numerous supernovae within the last 300kyr?

Firestone (2014) asserted evidence for numerous (23) nearby (d<300pc) supernovae (SNe) within the Middle and Late Pleistocene. If true, this would have strong implications for the irradiation of the Earth; at this rate, the mass extinction level events due to SNe would be more frequent than 100Myr. However, there are numerous errors in the application of past research. The paper overestimates likely nitrate and C-14 production from moderately nearby SNe by about four orders of magnitude. Moreover, the results are based on wrongly selected (obsolete) nitrate and C-14 datasets. The use of correct and up-to-date datasets does not confirm the claimed results. The claims in the paper are invalid.