Trivia / Ace Attorney Investigations: Miles Edgeworth
Development Gag: Edgeworth reconnects with Penny Nichols, a minor witness from the first Ace Attorney game, in "The Grand Turnabout". Edgeworth notes internally that while he spoke with her numerous times, he had completely forgotten who she was until she introduced herself again. This is a reference to the fact that even the development team found Penny so utterly forgettable that simply remembering her name was considered a mark of accomplishment.
Also falls under Fan Nickname: The Let's Translate on YouTube, also done by a fan of the series and one who worked on the Fan Translation team, uses the following localized names:
Teikun Ou = Di-Jun Wang
Gai Tojiro = Victor Rook
Manosuke Naitou = Horace Knight
Mikiko Hayami = Clara Harkens
Hakari Mikigami = Angela von Jure
Yumihiko Ichiyanagi = Raymond Furst
Tateyuki Shigaraki = Atticus Stalwart
Souta Sarushiro = Simeon Traill
Shuuji Orinaka = Louis Cage
Marie Miwa = Jennifer Reese
Ryouken Houinbo = Canis Fang
Issei Tenkai = Lee Tone
Tsukasa Oyashiki = Aria Manor
Isaku Hyoudou = Bill Rime
Paul Holic = Philippe Holic
Delicy Scone = Delicy Scones
Yutaka Kazami = Gus Takovski
Wataru Shirase = Han Dover
Touko Mutou = Sugar Pill
Otome Itami = Virginia Aochi
Tsubasa Kagome = Ann Tiggany
Bansai Ichiyanagi = Oswald Furst
Borumosu = Bullmoth
Shimon Aizawa = Marcus Ward
Ryuji Kamei = Paul Enicies
Ami Aizawa = Belle Ward
For the game itself: Ace Attorney Investigations, before that title was bestowed, was called Perfect Prosecutor by the fandom (though early announcements in Nintendo Power magazine also used that name).
Gumshoe had been 'Gummy' to the fandom for years beforehand, but Kay makes the nickname canon.
Detective Badd is usually referred to as "Detective Baddass", simply because of how much of a Badass he is.
Milestone Celebration: The main reason Frank Sahwit was added to the second game was because of the series's tenth anniversary.
Name's the Same: Jacques Portsman's Japanese name, Makoto Yuki, is very, very close to the name of Persona 3's protagonist, Makoto Yuuki.
Serendipity Writes the Plot: Edgeworth's flashback to the DL-6 incident in the 4th case is masked heavily and bordered by a "cloudy" filter (in addition to the series standard of merely putting flashbacks in black and white) to hide the fact that it is reused from the original GBA game (and thus has a 240 × 160 resolution with a 15 bit color depth on a 256 x 192 screen with 18 bit color depth) while Investigations is otherwise free of such sprite reuse (contrast Apollo Justice, where such reuse is very blatant when it occurs).
This also explains why Gumshoe looks exactly the same except for his tan coat. Gumshoe was dressed that way in Trials & Tribulations during case 4, which takes place in the same relative era. Back then it was due to the inability to fit an entirely new sprite in the game for a character who already exists so they just did it via Palette Swap. The DS has considerably more storage space for sprites but Gumshoe still retains the same physical appearance because that's what he looked like as told by the third game.
Concept art for Shi-Long Lang featured him shirtless, with the constellation of Orion scarred on his chest. Seems the director objected to the toplessness, even after a feather boa was added to cover the nipples.
A trailer shows Kay appearing in Turnabout Airline. Whether this means Kay would have first appeared earlier, or that Turnabout Airlines was originally a later case, is anybody's guess.
Originally the concept of the game involved Ema Skye as the protagonist and the game would focus on forensics tactics.
Concept art sketches show that Quercus Alba's design went through a phase with him looking much more like a gnarly old tree.