Neutrinos come in several "flavors." The "mixing angle" describes how rapidly the flavors of neutrinos change. Too few neutrinos were observed coming from the sun, the so-called "solar neutrino paradox." This is now known to result from the fact that many of the neutrinos coming from the sun change their flavor, so that they were not being detected. It was thought that this change of flavor occurred in the vacuum of space, but now it is known that this only occurs in the presence of matter. Therefore a considerable fraction of the solar neutrinos are interacting with matter in their travel from the sun to the earth. This is a surprise, because it was not thought that neutrinos interact this readily with matter. See Neutrino Oscillations for a discussion of neutrino oscillations in matter.The results also show that another property of neutrinos, related to how they interact with matter, known as the "mixing angle," must be large, rather than small, contrary to what physicists believed until quite recently.
If neutrinos interact with matter, they could also be influencing matter. Because there are so many neutrinos, they could be having a considerable influence. This could impart energy to matter and slightly destabilize it, or this interaction could have the form of a quantum "observation" that might collapse the quantum energy state associated with matter. Either effect could conceivably influence radioactive decay rates. (See "Furtive Glances Trigger Radioactive Decay," Science 2 June 2000 vol 288 page 1564.) Or there could be other as yet unknown interactions of neutrinos that have such an effect.
If there had been a nearby supernova in the recent past, then there would have been many more neutrinos, and this could have sped up radioactive decay rates. This would have led to higher levels of radiation in the past, and could help to explain why dates based on radioactive decay tend to give values in the hundreds of millions of years.