Could Have Avoided This Plot: As part of the "honesty is the best policy" lesson presented in the first story, Twilight writes that if everypony had been more open and trusting of each other, the case would have been solved much more quickly. In fact, there wouldn't even be a case if the thieves had just asked Rarity for the gem in the first place.
Anyone you're interrogating or confronting, if you screw up.
Dude, Where's My Respect?: Twilight lampshades this, pointing out her exploits—particularly the ones that could have been prevented, or at least made simpler, if ponies had listened to her—and then asking (loudly) why nopony listens to her even after all that. Rarity gives this a Hoof Wave by suggesting ponies probably just think she's due to be wrong after being right so much.
Epic Fail: Everything the Canterlot Investigation Team does. Last time they were in Ponyville, they accused Derpy of 'Grand Theft Muffin', tried to find a dragon egg smuggling ring. This time, they fail at taking a train. A train that only has two stops.
Fourth Wall Observer: Pinkie Pie is given this attribute, common to her in fanon, so that she can do the tutorial. She says she has a "walkthrough"; Twilight has no idea what that means.
Genius Ditz: Discussed; Twilight is flabbergasted by the Diamond Dogs' keen and frequent understanding of legal procedures, such as demanding she produce a search warrant before she starts investigating their caves, that she can't help but point it out internally. Their fascination with shiny things shows they're still otherwise the same old dull-witted dogs.
Hoof Wave: You'd think Twilight of all ponies would be able to get others to trust and believe her, but nope; that'd make the game way too simple and boring, so it gets explained away by Rarity that the ponies probably think Twilight's just due to be wrong sooner or later after being right so much. Though whether this is the case or just Rarity's suggestion is up in the air.
Jumped at the Call: Twilight is so determined to prove herself a capable investigator that she wastes no time trying to crack the case on her own. While she does manage with what little professional experience she has, this leaves her underprepared for any legal procedures she must undergo.
Lampshade Hanging: There's the occasional nod to game mechanics that make no sense in-universe, like Twilight wondering why she's carrying around a picture of the Diamond Dogs.
Police Are Useless: The Canterlot investigative team called in to solve the case in Ponyville are very incompetent, and everyone in Ponyville knows it; for instance, they once implicated Pinkie Pie in a dragon egg smuggling ring that didn't even exist. All the more reason for Twilight to crack the case before they do. At the end of the first chapter, they finally arrive nowhere near Ponyville; an astounding feat, considering the Ponyville train line only has two stops, and one of them is in the town proper.
Race Against the Clock: Twilight only has a few days—and later just one day—to solve the first case before the investigative team from Canterlot arrives. And judging how they once spent Celestia knows how long searching for a "missing" baby that was safely hiding in a closet, she and her friends have every reason to panic.
Reasonable Authority Figure: For all her incompetence and initial aversion to the idea, the Mayor is willing to make Twilight an official Ponyville Investigator after Twilight proves herself.
Reset Button: If you fail a confrontation, choosing to try again essentially causes this by starting it over with no acknowledgement of it happening besides an internal comment from Twilight.
Reverse Who Dunnit: The very first cutscene of the game shows the silhouettes of the culprits, and you spend the entire first case just trying to prove it so Scootaloo doesn't get the blame.
Screw the Rules, I Make Them!: A heroic example. Being the mayor of a town that has no police force, the Mayor comes to the realization that she has the authority to bend the law in that field, and uses "the power vested in [her]" to make Twilight a temporary investigator so she can be given a search warrant, just like that. She also takes on declaring the verdict for the accused party in the end, despite not being a judge.
Sexophone: When Rarity tries to '...sort things out, if you catch my drift' with the Diamond Dogs' guard dog, the soundtrack briefly switches to a saxophone melody.
The Slacker: The Mayor does anything but actual work when at her office. That's not to say she's incompetent, though.
Spanner in the Works: Scootaloo serves as this for the thieves' plan, as her chance appearance startles them into making a hasty retreat when they steal True Blue, leaving behind the evidence needed to implicate them. Opalescence also fulfills this role, her hair and bow leaving a trail to the culprits.
Super OCD: For once, it's not Twilight. Rarity cleans up her boutique completely, even though it is a crime scene, because she can't stand the disorder.
Taught by Television: Twilight apparently learned all of her investigative skills through mystery novels.
Terror Hero: The Diamond Dogs see Rarity as this, her mere presence triggering unwanted memories of their last encounter. The whole reason why they try to steal True Blue in the dead of night, rather than take it by force as they normally would, is so they won't have to deal with her.
Turn the Other Cheek: Twilight writes in her friendship report at the end of the first chapter that repaying cruelty with kindness is the most effective way to catch someone off guard. Rarity demonstrates this by letting the Diamond Dogs keep True Blue when she learns it originally belonged to them and were just trying to get it back.
Villainous Breakdown: Well, not exactly villainous in this case, but there's a "breakdown animation" near the end of the case. Rover starts screaming, causing gems to fall down from the ceiling of the cave. Fido and Spot run away, leaving Rover standing there getting hit by gems. Finally, a larger gem than the others crashes down on Rover's head, causing him to fall over.
"Yes"/"No" Answer Interpretation: When Apple Bloom doesn't look convinced at Twilight Sparkle's promise not to tell anyone what she just told her, she promises it with a Pinkie Pie swear from the show: "Cross my heart and hope to fly, stick a cupcake in my eye." The response this gets is, "That a yes?"