1912:

The Librarian, first film to feature a librarian

1919:

A Very Good Young Man, first film to feature a male librarian

Notable: The main character’s profession was changed from brass bed factory worker in the play to librarian in the film

1921:

The Lost Romance, first film to feature a librarian with glasses and a bun (the Spinster Librarian image begins!)

1932:

Forbidden, first sound film to feature a librarian

Notable: “Old lady foureyes!” In the film’s opening scene, two small boys shout this as public librarian Lulu Smith (Barbara Stanwyck) walks down the street.

1932: 

No Man of Her Own, first film to feature a librarian in undergarments

1933 & 1940:

First films to feature a librarian saying, “Shush!”

The Good Companions, 1933 (UK)
The Philadelphia Story, 1940 (US)

1943:

The Seventh Victim, first horror film to feature a librarian

1953: 

Pickup on South Street, first film to feature an African-American librarian

1984:

Cal, first (non-erotic) film to feature a nude librarian (Helen Mirren)

Source: Several items of trivia in this post I gathered together while reading The Image of Librarians in Cinema, 1917-1919, by Ray Tevis & Brenda Tevis, 2005, a great source for information on reel librarians.