According to Robert Anton Wilson in Cosmic Trigger vol II the reason James Joyce chose June 16, 1904 as the day on which to set Ulysses is actually because that was the day on which Joyce and Nora Barnacle first had sexual relations of a sort (she masturbated him).
As Wilson puts it "Ireland remains Catholic and very, very, puritanical.It is Joyce's last and funniest joke that he has, by the sheer force of his genius and international reputation, tricked them into commemorating a Hand Job every year on June 16".