A lot of details went into the researching behind the locations, schools and universities that appear in the Tsubasa Reservoir Chroniclereal-world AUFreefall, as well as the symptoms of leukaemia, which a main character is diagnosed with early in the plotline.
Between Minds (Portal and HalfLife) is packed with this with everything from helicopter specifications to language translations to first aid to building layouts to real-life weapons to cut game material to the actual mechanics of an EMP.
Child Of The Storm takes it up a few notches and shows that this part of Nimbus Llewelyn'sSignature Style. The story uses historically accurate Norse titles and foods, drawing on a lot of minor throwaway details from obscure corners of each of the canons and displaying an awareness of basic physics (in chapter 54, Harry is flying on a souped up Firebolt, which, in the interests of fairness, can't exceed its production top speed on the Quidditch Pitch. Harry considers that he'd rather not find out what would happen to him and the broom if he suddenly lost a third of his speed, and skirts the Quidditch pitch).
It also displays awareness of certain political realities - for instance, it is abundantly clear in earlier chapters that Harry feels that he has a very large bone to pick with Odin, and it is repeatedly pointed out to him that Odin is an absolute ruler and cannot/will not accept such levels of defiance in public, even from his grandson. In private, under certain circumstances, he is rather more accommodating and understanding, the implications of Younger than She Looks where an attractive teenage girl is concerned and uses the exploration of consequences of the basic premise (Harry is the son of Thor, who was incarnated as James Potter in his first shot at humility) of the fic as the engine of the plot.
In the My Little Pony: Friendship Is Magic fanfiction Silent Knight, Nightfyre's flightsuit puts constant pressure on her limbs, ensuring proper blood-flow to the brain during stressful maneuvers. This is the same way real life flightsuits work for jet and fighter pilots.
In the same chapter, Ash Coat notes some materials on the human sword that genuinely act as absurdly sharp material when treated correctly; it's suggested that some Applied Phlebotinum is employed to sustain this condition.
Cornova did a lot of research with regards to the ins and outs of the Pokémon anime for Poké Wars.
A prime example is how he included an entire chapter on Kaiza, a character from an episode of Pokémon that never made it out of Japan.
Also, numerous one-shot characters (Duplica, Yas and Kas Gyms, AJ, etc.) are portrayed perfectly in character.
The author behind XSGCOM has an author's notes section after every chapter, where he/she explains from exactly where in the original works every character, plot-twist and gadget in the chapter came. He does the same for Hunted Tribes and New California Dreaming.
The Total Drama fanfic writer, Gideoncrawle shows his work routinely. In his first story, Legacy, this is most apparent in the details related to the victim's wound. His later stories have substantial Notes sections that explain the more obscure allusions, among other things.
His Season 1 reimagining story, The Legend of Total Drama Island tends to show his work in-story for such things as inventive solutions to certain problems, and the effects and treatment of hypothermia.
In most of the New Look Series the author, Shinnok Raiden 99 has well-conceived characterizations for its main characters and a healthy amount of mythology gags.
One of the reasons the Homestuck fan blog Brainbent is so popular with fans is because of how accurately and sympathetically it portrays people with mental health issues (except John, who's disorder is unspecified). In particular, Autistic readers really like the non-stereotyped portrayal of Autism.
Friendship Is Optimal has a lot of accurate science, and the author has clearly done a lot of research on artificial intelligence and philosophy.