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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 E25 "Party of One"
Alternate Aesop Interpretation: At first, it looked like this episode was steering towards the aesop "just because your friends don't want to play all the time doesn't mean they don't care about you any more," or "sometimes real life takes precedence over partying." Her friends' evasions and excuses seemed perfectly sympathetic even before we knew they were planning a surprise party; many people, especially introverts like Twilight and Fluttershy, would not want to go to a big party the day after they just had one. Plus, people do have to work and sleep at some point.
Ear Worm: "This is your singing telegram, I hope it finds you well. You're invited to a PARTY 'cause we think you're really swell..."
Fridge Brilliance: Pinkie Pie starts to sweat and slow down her singing invitations during her visit to Rainbow Dash. While this might be the result of her many costume changes, it more likely that she was burnt out as a result of being at a higher altitude.
Alternatively, it could just be that she was getting tired from running back and forth all over Ponyville and singing her invitation song five times in a row.
Sir Lintsalot is Rarity (posh, upper-class british accent, apparent high-class attitude)
Madame Le Flour is Fluttershy (quiet, timid sounding voice)
For some reason, Twilight and Spike are left out.
It's possible that, at this point, Twilight and Spike haven't been in town long enough for the mentally-unstable Pinkamena to think to replicate them, Pinkie's friendship with them not yet being deep enough to affect her crazy side if you will.
Applejack, the Element of Honesty, was never fully lying. Rainbow Dash WAS bringing supplies (for the surprise party), and they were indeed constructing a new interior for the barn (specifically, constructing a surprise party).
However, it's far harder to justify her initial excuse to get out of Gummy's after-birthday party - obviously, she hadn't spent the whole afternoon apple-picking.
Fridge Horror: After Pinkie snaps, she invents a bunch of new friends to attend Gummy's after birthday party, one of which is a pile of rocks named Rocky. When Rainbow Dash arrives at her house, she knocks over said pile of rocks, essentially killing Rocky.
Harsher in Hindsight: A rather infamous FiM fanfic 'Cupcakes' features a psychotic Pinkie Pie mutilating and torturing Rainbow Dash to death, in horrific and gruesome ways. That doesn't happen in this episode of course, but Rainbow Dash being alone in a room with a deranged and possibly violent Pinkie Pie made fans familiar with the fic more than a little uncomfortable.
Here's one not "Cupcakes" related: At the time, Pinkie's breakdown was one of the scariest cases of a mane character going crazy in the series. Not no more!
Idiot Plot: The episode hinges on Pinkie Pie forgetting her birthday, which is understandable, because she's Pinkie Pie. To a lesser extent, there's also the fact that a surprise party was being thrown in her honor with nobody running interference, nor any other countermeasures to deal with the fact that Pinkie Pie could catch them setting up (even when they had to pick up a cake at her home/place of employment).
Nightmare Fuel: Pinkie's party with her imaginary friends. It really doesn't help that she's made a distinct and reasonably developed personality for each. This leads to some Fridge Horror when you consider how lifelike they are from Pinkie's POV. They have their own personalities, conflict with each other, and have a conversation with Pinkie as if she considered them fully intelligent people. And all of this in a few hours at most, it's scary when you consider how easy it it is for Pinkie's mind to snap.
Her breakdown near the end. If Rainbow hadn't arrived when she did...
You don't need to deplore the others' actions to feel sorry for Pinkie. This series is perfectly capable of showing complex enough interactions that they lead into conflict without having anyone suddenly become nastier for no reason. But just because it's mostly happening in her head doesn't make it any less serious for her.
The Woobie: Pinkie Pie is so depressed her hair deflates. She is in serious need of a hug at the mid point.