Rainbow's desperate words when Phoenix meets her again in the detention center are reminiscent of Larry Butz's during Phoenix's first trial, right down to "There's nothing left for me in the world!/Equestria!"
The brochure for the Equestria 500 in Part 3 - Twilight also has them.
Sonata is named after the Ludwig van Beethoven piano piece Moonlight Sonata. To drive this home, the actual piece itself plays when Sonata admits to the murder.
Derpy, after bringing up Phoenix not knowing pegasi could move clouds, says "Oh how I laughed and laughed!" Phoenix's response is to think "Except I wasn't laughing...". This is almost a word-for-word recreation of part of the lyrics from Portal 2's ending song, Want You Gone.
invokedPinkie suggests that there are possibly two Rainbow Dashes, resulting in this double rainbow reference:
Phoenix: Double Rainbow Dash? Pinkie: All the way! That would be so intense!
Pinkie then suggests that this twin's name is Wob Niar, mirroring Maya's theory about a fake Phoenix Wright named Xin Eohp in Trials and Tribulations.
This becomes a Brick Joke in Part 5 when Phoenix bumps into a pegasus who looks almost exactly like Rainbow Dash, but has the same skin color, accent, and attitude as Furio Tigre, who turned out to be Phoenix's impersonator and own "Evil Twin" in one case.
Apparently, Rarity's middle name is Tabitha, her voice actress' name in the actual show.
Rarity gives a shout out to the brony community in episode three, saying she "tried to love and tolerate" a crying child who was driving her nuts. A common brony response to an anti-brony is "I'm going to love and tolerate the shit out of you!"
During a discussion about why the Judge goes by "Judge" outside of the courtroom, he states that it's a simple, one-word name, like that one singer, you know, "Living Material World!". And then the scene cuts to a picture of Rarity.
Also possibly a shout out to Ponies The Anthology, in which that very song is set to a montage of Rarity clips.
Can also be a shout out to the Film version of Inspector Gadget where Claw names himself such because of said singer.
Lenora: "Sparkle, Sparkle, Sparkle!" She didn't have to yell at me. It's not my fault pony names are hard to pronounce!
Whilst looking for Trixie after winning the case, Phoenix encounters a strange, pale-green and white unicorn mare who shyly tells him that she really likes his hands before leaving a bemused Phoenix alone. This is an obvious shout-out to Lyra, Ponyville's resident human fanmare/fetishist in the brony fandom.