Trixie: "You can't be serious. Of all the convoluted, contrived, confounding coincidences, this one has to be the least profound, least precise, least possible possibility ever postulated by ponykind. It was just somepony setting off...a firework or something. Nothing at all like this...phenomenon you call a Rainboom. Puerile! Psychotic! Preposterous!"
Because You Were Nice to Me: Derpy ends up taking Trixie's side in the seventh contest because Trixie didn't gawk or make fun of her eyes when they first met.
The Chessmaster: Twilight Sparkle seems to outdo even Celestia in this fic. She places Trixie's scry spell on a photo in Trixie's bag to listen in on her, faking Stalker with a Crush behaviour and invokingLoophole Abuse in order to test Trixie's determination and compassion for her. This shows up even earlier when she actually uses her magic at full power for once in the third trial in order to gain the rights to spend time with Trixie through more Loophole Abuse, so she can learn more about her and finally become friends with her.
Competitive Balance: The purpose of the seven tasks in a Magician's Duel is in acknowledgement that magical prowess can manifest in different ways, and the three most prominent unicorns in the story illustrate this in different ways.
Unskilled, but Strong: Twilight Sparkle has the most raw magical power known to exist short of the Princesses, but is more likely to rely on that than any sort of finesse.
Weak, but Skilled: Rarity is capable of incredibly fine detailed work as part of her fashion business, but can't come anywhere near Twilight's or Trixie's strength levels.
Jack-of-All-Stats: Trixie has neither Rarity's precision nor Twilight's raw strength, but still performs very well in both areas, and that balance allows her to officially retain the title of Great and Powerful.
Over Nine Thousand: At the tournament, Twilight's magic point average is revealed to be this.
Pair the Spares: Defied when Trixie and Pinkie are talking about the relationships their friends are in.
Trixie: "I suppose next youíll tell me Applejack and Rarity are-"
Pinkie: ďOh ho ho, oh no, ha ha ha, noooooo no, wow, thatís just...thatís probably the silliest thing Iíve ever heard, those two? Ha HA, thatíd be a laugh. Ahhhh, oh Trixie, youíve got some crazy ideas.Ē
Relationship Upgrade: Derpy and Fluttershy had this before the story began, as did Rainbow Dash and Pinkie Pie. By the end of the story, Twilight and Trixie have gotten here as well.
Serious Business: Titles are prestigious enough that there are formal rules regarding how they are transferred and competed for, and seventy unicorns end up competing for "Great and Powerful" in the tournament. And the subsequent victor will spend the rest of their life stalked by challengers. Said rules have a few useful loopholes to avoid most of the hassle, though.
Walking the Earth: Trixie does this near the end of the story to become a more powerful unicorn. By the end of the fic, she has to do it again because it's a requirement of winning the title of Great and Powerful. Fortunately, Twilight pulls her Loophole AbusingXanatos Gambit at this point.