Framed Clue

The main character is looking at a picture, trying to figure out a clue in it. In frustration, he throws it down, breaking the frame... and there, inside the frame, is the clue—a Treasure Map, or a letter from the person who took the picture, or something else that fit behind the picture itself.

A variation is when the frame gets broken accidentally, usually due to The Fool knocking it over.

Examples of Framed Clue include:

Comic Books

Present in The Secret of the Unicorn. For some reason, bad people really want 3 scale models of a ship. When Snowy accidentally breaks one, Tintin later discovers that a secret scroll was hidden under the mast.
In Bizenghast, the letter that exonerates the matron ghost of her crimes and allows her to move on is painted into a portrait in Dinah's room of the matron ghost.

Film

The Goonies. After Mikey finds a framed Treasure Map in the attic, he hands it to Chunk--The Fool—who predictably breaks the frame by dropping it.
In Paycheck the stamp on the envelope that held the 13 clues was in fact a clue itself. In fact one of the clues in the package's only purpose was to help him notice the stamp.
Saw II has a photo taped to the back of a frame. And for extra kudos, it's also marked with an 'X'.
In What Lies Beneath, Claire discovers a newspaper article relating to the ghost on the back of a photo in a frame, after said ghost knocks the frame to the floor for the second time. The ghost, Madison, is deliberately attempting to guide Claire towards the clues.

Literature

In the first Mrs. Murphy and Tee Tucker novel Wish You Were Here by Rita Mae Brown one of the citizens of Crozet discovers an important clue behind a framed poster.
The mystery novel The Face of the Man from Saturn by Harry Stephen Keeler concerns a painting of a bizarre extraterrestrial. Someone breaks into the shop where this painting is stored, kills the owner, and then cuts the Saturnian's face from the canvas ... and steals this, leaving the rest of the portrait. The detective discovers that a message revealing the location of treasure is concealed beneath the portrait's face. But there were two copies of the painting, and the killer stole the wrong one.

Live Action Television

Variation in Heroes, in which Chandra Suresh's diary is hidden inside the case of his laptop, and only discovered when Mohinder throws it down in frustration.
In the Australian series Mission Top Secret, one of the main characters discovers a clue this way.
Salute Your Shorts has a subversion in that the picture frame breaks, and there is indeed a treasure map inside... planted by Budnik, who was the one to break the frame in a scheme to sell copies to the fake map to fellow campers.
A variation occurs on an episode of Bones. Hodgins is taking samples from a crime scene and when nobody is looking opens up a frame and removes a picture that showed him and the victim together before anyone noticed. In an aversion, the picture is NOT a clue related to the case, but would have revealed Hodgins past connection to the victim (childhood friends until he stole Hodgin's fiancee) and stopped him from helping to solve his old friend's murder.

Video Games

A seemingly pointless minigame in Hotel Dusk: Room 215 ends when Louis breaks a potplant with a hidden key.

Western Animation

Foster's Home for Imaginary Friends has Mac and Bloo finding the map to the Foster's treasure this way.