Both a Blue Moon and lunar eclipse occured on the same day
The next such event to happen on New Year’s eve will be in 2028.

Date skipped in Kiribati
The Phoenix Islands and the Line Islands in Kiribati skip December 31st due to a change in their time zone from UTC−11:00 to UTC+13:00 and UTC−10:00 to UTC+14:00, respectively.

Coup in Nigeria
A military coup in Nigeria overthrew the civilian government of Shehu Shagari and installed Maj-Gen Muhammadu Buhari.

Manhattan Bridge opens for traffic
The Manhattan Bridge, one of the first suspension bridges ever constructed, was opened to traffic on this day. The bridge was designed by Leon Moisseiff and crosses the East River in New York City.

The first annual ball drop at Times Square
The annual tradition of dropping a ball at 11:59 pm to mark the start of the New Year was organized for the first time by Adolph Ochs, the owner of the New York Times.