Pinkie Pie: It's my tail! It's my tail! It's a-twitchin' twitchin'! And you know what that means! Twilight Sparkle: Actually, Pinkie, I haven't the slightest idea.
Written by Dave Polsky
Twilight Sparkle learns that Pinkie Pie has an unusual ability to sense happenings in the immediate future based on twitches and tics of her body, known as "Pinkie Sense". Twilight is skeptical, but much to her frustration all of Pinkie's predictions seem to come true... and even more frustrating is that they all seem to target Twilight for some reason, whether it's falling objects, slamming doors, or an alligator in the bath tub.Twilight tries to investigate Pinkie's so-called abilities with the intent of disproving them, but her efforts are hampered by her own impatience and a series of slapstick disasters, all of which are seemingly predicted by the Pinkie Sense. There's clearly a pattern going on, but Twilight stubbornly refuses to admit it. When Pinkie suddenly predicts "a doozy" of an event happening in the Froggy Bottom Bog, Twilight tags along with her friends only out of concern for Fluttershy, who had earlier gone there to help some frogs find a new home.The gang finds Fluttershy safe and sound in the marsh, and Twilight is all set to rub it in that the Pinkie Sense has apparently failed... but she never gets the chance, as a vicious hydra emerges from the swamp and attacks! A frantic chase ensues, and Twilight is forced to buy time for her friends to get to safety. Twilight herself only escapes the hydra by trusting in the Pinkie Sense and making a literal leap of faith. Much to Twilight's bafflement, it turns out the hydra attack wasn't "the doozy" Pinkie had predicted, but she's too worn out to be angry for long. Twilight finally admits that Pinkie's senses are real, even if she doesn't understand how or why they work. And guess what? The "doozy" Pinkie predicted was Twilight admitting she was wrong.Later, Twilight prepares a letter to Princess Celestia with her lesson for the day (that there are some things you don't have to understand completely to accept as real or true), then goes to hang out with Pinkie. Her Pinkie Sense is telling her there'll be another falling object today, but she and Twilight are prepared. Spike, however, is not prepared for Princess Celestia literally dropping in to pick up Twilight's report in person.
Tropes present in this episode (YMMV tropes can be found here):
Absentee Actor: Rainbow Dash and Rarity are both absent in this episode.
Agent Scully: Twilight becomes this, refusing to accept that Pinkie's "Pinkie Sense" is real up until the very end of the episode. Part of her problem is that she's more interested in being right than in finding the truth.
Anvil on Head: A flower pot, a big anvil, a hay cart, and then a piano fall over Twilight Sparkle. Justified in the best way possible, as they all fell from a sky delivery truck managed by a group of bumbling pegasi, one of whom is DerpyHooves.
Ascended Meme: This would be the first episode (and generally at least once in every following episode to date) where Derpy Hooves is present with the derped eyes that she was accidentally given in the very first episode "Mare in the Moon". She had appeared in several episodes but lacking the derped eyes. Here, she's even given a job as a delivery pony, tangentially related to the fandom's take as the Ponyville mailpony.
Blowing a Raspberry: One of the Hydra's heads sticks its forked tongue toward the ponies as they give up the chase.
Bomb Whistle: At the conclusion of the episode, Spike steps outside to send off the letter to Celestia, while Pinkie announces her Pinkie Sense has just detected another imminent falling object. Cue the whistle, and Spike looking up in terror. However it's just Celestia, who makes a controlled, if thunderously hard-landing. She then picks the scroll out of his claws, and takes off again.
Twilight could have easily teleported past the broken platforms (even though she was able to teleport out of the last adrenaline-pumping chase she was in). Twilight can also telekinetically carry an Ursa Minor and a water tower several miles without a line of sight but not herself for a few yards to a point she can see. This could possibly be due to being overcome by fear.
Fluttershy doesn't just fly over for some reason. Though, similar to the case above, it may be justified in this case, as the last time she tried to fly when she was scared her wings locked up.
For Science!: A benign example, but it's still shown as the wrong approach. Twilight observes Pinkie Pie and makes correlations between body twitches and what they signify but she can't figure out the connection between the twitches and the events.
Furry Reminder: At one point, Pinkie rolls around in the grass. You may think it's just her randomness, but real horses do that a lot.
Gravity Is a Harsh Mistress: Pinkie Pie shudders her way right off a cliff, only to get yanked back by Applejack. Gravity fails to grab her for long enough that you'd almost think her shudders would get her across the gap on their own.
Growling Gut: Pinkie's stomach growls once in this episode, which winds up causing a loophole.
Pinkie Pie: What's not to believe? You do magic, what's the difference? Twilight Sparkle: Huge! For one thing...[stands on soapbox] magic is something you study and practice. It only happens when you decide to do it. It's meant to make something specific that you want to happen happen. With you, ugh, it makes no sense at all! Pinkie Pie: That's so not true, Twilight! [beat] Sometimes it's a bunch of random things happening to my body at random times that supposedly predict the future. I call 'em "combos".
The Load: Spike. He can't keep up with the rest of the ponies on foot as they run and later gets stuck in the bog, requiring Twilight to run back to save him.
Made of Iron: Twilight falls down a ditch, gets slammed by doors, is stung by a swarm of angry bees, falls down a steep stairwell, then later takes a flower pot to the head, followed by an anvil, a hay cart and a piano. Still, she shakes it off within seconds and is fit as a fiddle and ready to go off on a rescue adventure. (OK, she's in bandages after a couple of these, and even ends up in a wheelchair at one point, but those are gone within a scene or two.)
Said adventure ends with Twilight falling down a cliff, landing on a big swamp gas bubble that sends her flying until she lands on top of a stone pillar, from where she bounces onto a second pillar, from where she bounces a second time until finally crashing against a solid rock wall. After a couple of seconds, Twilight shakes her head and she's fine again.
Mobile Shrubbery: Twilight uses this when spying on Pinkie. Turns out that Pinkie knew all along that Twilight was spying on her but said nothing to not spoil Twilight's "fun".
Science Cannot Comprehend Phlebotinum: Twilight runs herself ragged trying to analyze/disprove Pinkie Pie's "Pinkie Sense". In the end, she gives up and admits that maybe the "Pinkie Sense" can't be analyzed (which turns out to be the "doozy" that Pinkie predicted would happen). The point is that it exists, even though Twilight doesn't understand how it works.
Self Fulfilling Prophecy: Pinkie predicts that the "doozy" was going to happen at Froggy Bottom Bog, which leads the gang to investigate there. Had they not gone to Froggy Bottom Bog, Twilight wouldn't have admitted that Pinkie Sense was real there, which would have made her right about it in the first place. Then again, that would mean that Fluttershy is left to the mercy of the Hydra. That could have qualified as a "doozy".
Twilight's "Latin" name for Pinkie Pie sounds like a reference to the Roadrunner cartoons where they'd do the same, fitting since Twilight is stalking Pinkie Pie and in the process suffers much the same sort of injurious Humiliation Conga Wile E. Coyote often did. Meanwhile, Pinkie Pie, as usual hops around everywhere like Pepe Le Pew.
The cloud of apparently nasty smelling gas that appears when the hydra first shows up may be a reference to the original myth in which the hydra produced a deadly poisonous gas that constantly surrounded its lair.
Spider-Sense: The Pinkie Sense is an instinct that alerts Pinkie Pie to immediate danger.
Straw Vulcan: Twilight is so obessed with logic that she fails to see that the Pinkie Sense is a repeatable, reliable ability, that Pinkie Pie simply can't control.
Sufficiently Analyzed Magic: Twilight's rationale for why unicorn magic is believable, and the "Pinkie Sense" isn't; unicorn magic is something that is practiced and studied while the Pinkie Sense is random and innate.
Surprise Creepy: Mostly a silly, funny episode... then the hydra shows up. Though it has its own brand of silliness, with one of the heads being slow on the uptake.
Wacky Sound Effect: Spike, backing out of the library's main door with a stack of books, emits the same "backing up" alarm that vehicles like delivery trucks and forklifts make.