This is more like Chekhov's Habit, but there's a Running Gag in Hunting The Unicorn of David writing down everything relevant to the Warblers (and especially Blaine). It proves useful when he has hard evidence that Blaine has a stalker.
In the Transformers fanfic series Black Crayons, Ironhide begins teaching Annabelle how to speak Cybertronian. First, it is a cute way learn about the Twin's pranking plans. Later, it becomes a life saving skill when she overhears a key piece of information from Starscream.
Jack's ability to memorize fingerprints on things to distinguish them from similar things helps him put out a fire at Dr. Brainstorm's lab in Calvin and Hobbes: The Series.
In the second chapter of A Growing Affection Hinata suggests Naruto work on chakra control by trying to create a tiny Rasengan on each finger tip. This becomes the Five-Points Rasengan jutsu, and shows up multiple times in the story, including the final battle.
Legacy Of The Rasengan: Naruto has KazeKiwa no Jutsu. In this fic it's one of Naruto's signature moves and sees a lot of use. It ends up inspiring Naruto to create the Rasengan since the mechanics of both are similar (no hand signs, spinning chakra, very good chakra control). Also helps Naruto in his fight with Neji since it made it easier for him to concentrate his chakra enough to mimic Neji's fighting style and rip through his Rotation.
Regeneration in Children of Time: Kit Bennett reveals herself as a Time Lord, and the Daleks torture her to study a Time Lord's use of regenerative energy. At the climax, Kit uses a burst of that energy to knock out the Daleks' computers, destroying Dalek Caan in the process. Then in the season finale, baby Katherine, who will grow up to be Kit, heals her dying father and half-dead godfather.
In Break My Fall, Red spends his lunches helping out at the nurse's office. This later becomes important when he has to rush to the nurse's office after school hours to get supplies to treat Green's self-harm wounds.
In Despair's Last Resort, Naomi is established as being the Super High School Level Translator, who knows ten languages. As she's dying, she uses her blood to leave a dying message. But in order to hide it from the killer, she leaves it in French. This allows the one living student who knows French to pick out who the culprit is.
Takara's experience as a journalist helps her out in the investigations.