Loved doing this research. Was amazed to see how many things happened on Jan 2 over the decades, centuries... um... since AD 69!
For some odd reason, I found this one the most randomly fascinating-
1890 Record 19'2" alligator shot in Louisiana by E A McIlhenny
BTW- I found this fact on http://www.onthisday.com/events/
Which web sites did you use?