These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: My Little Pony: Friendship Is Magic S1 E6: "Boast Busters"
Accidental Aesop: Though the official moral is that it isn't arrogant to use your talent when you need to, another lesson might be "Those who boast will eventually be called on it."
Trixie doesn't so much get in trouble for boasting as she does for lying, had she not told a fib about beating an Ursa Major there would had never been anything to prove her wrong.
Anvilicious: Whatever way the Aesop is taken, it seems Ponyville does not take kindly to boasting.
Ensemble Darkhorse: Outside Celestia and the Mane Six, Trixie's popularity is rivaled only by Luna and Derpy/Ditzy, to the point some have called for her to become a recurring character.
Trixie In A Leather Saddle: Trixie is probably the biggest Draco in Ponyfandom, easily edging out Gilda and Discord. Probably attributable to the fact that unlike Gilda, she didn't do anything to Fluttershy, the fact that she's rather more adorable physically and with her mannerisms than either of them (despite being at least as big a jerk), and for the scale of what she did compared to what others have done, gets the harshest karmic retribution.
Also, astronomy buffs might notice that the Ursa has a certain constellation on its flank...
Also, the Ursa Minor has a long tail, just like in the myth of the constellation.
It also takes a rudimentary knowledge of Latin to know that 'ursa' means 'bear,' and that Ursa Major and Ursa Minor are the official names of the 'Big Dipper' and 'Little Dipper,' respectively.
This could also be seen as Foreshadowing for the reveal at the end...
Hilarious in Hindsight: In this episode, Twilight's genuine magic beats out Trixie's parlor tricks. Two seasons later, Twilight's parlor tricks beat out Trixie's genuine magic. She just cannot catch a break.
The Woobie: Twilight Sparkle thought her friends would hate her after showing her magic since Trixie's magic show.
Jerkass Woobie: However while Trixie herself was showing off, she suffered a slight guilt and admitted to lying just to make herself look better. In Season 3, where she returns in "Magic Duel", we find out that she did have it rough after the events of this episode.