I do not believe the calendar we are using now existed at that time so the exact date being missing is not that hard to believe. And lunar calendar's float all over the place. The Jewish calendar is/was a lunar one but they lock it with the solar calendar to keep their holiday's roughly the same time each year. The Muslims use a pure lunar calendar which is why Ramadan moves around every year. The crucifixion is tied to the Jewish Passover so that is why it is somewhat variable.
However, if you go backwards and figure out which year he died in, you should be able to figure out when Passover was that year and get an exact date if that's what floats your boat. The video in the OP seemed to be another 'look at me, I'm an atheist and this is why your religion sucks' type video.
