This episode contains examples of the following tropes.
Ambiguous Syntax: Piglet and the others are surprised to find out that the "horse thieves" are actual horses that are thieves.
And Then What?: Jack is upset when he rips off Piglet's sheriff badge, since it means he has no one to trounce. Piglet then suggests that he could become sheriff and clean up the town. Jack takes to the suggestion readily since he always wanted to be sheriff. (In-universe, he apparently really wanted the sheriff role in the play and when he didn't get it, his villainous role became his outlet for acting out.)
Badass Adorable: The Masked Bear puts up a decent defense against Jack's ice cream offense.
Be the Ball: Nasty Jack does this to one of the horse thieves when showing the difference between "bounce" and "trounce."
The Masked Bear steps into the bar right when Nasty Jack is about to trounce Piglet.
Subverted the second time; Christopher Robin assures Piglet that the Masked Bear saves him from Nasty Jack, but Jack merely dodges the Masked Bear and his Noble Steed when they charge toward him in a railway car. Tigger lampshades this and flips through the script since that wasn't there.
Cast the Runner-Up: In-universe, Jack wanted to be the sheriff but he became a horse thief instead. When Piglet suggests he could be the sheriff, Jack takes readily to it.
Chekhov's Gun: Nasty Jack can't trounce Piglet if the latter loses the sheriff badge. Then he accidentally rips off Piglet's sheriff badge, which makes Piglet no longer sheriff.
Continuity Cameo: Kanga, Roo and Kessie all appear at the start as audience to the performance.
Framing Device: The story is actually a play directed by Christopher Robin.
Knight of Cerebus: Nasty Jack is one of the few villains in the show that is a legitimate threat to the toys. He shows that he can and wants to trounce Piglet. Nasty Jack also plays with his food, as we show him "teaching" Rabbit how to make a banana split. While Pooh Bear manages to fend him off, Nasty Jack incapacitated him and Eeyore before challenging Piglet to a showdown.
Let's Get Dangerous!: Pooh Bear becomes The Masked Bear to save Piglet. He storms into the bar, politely asks Nasty Jack to freeze and engages in an ice-cream brawl with him.
Piglet: His name is Nasty Jack! Not Friendly Jack, or Perfectly Wonderful Jack, no! It's Nasty Jack!
Nightmare Face: Nasty Jack when he wields an ice cream carton against the Masked Bear.
Ninja Pirate Zombie Robot: Piglet and the others are surprised to find out that Nasty Jack and his gang of horse thieves are actual horses who are thieves.
No Celebrities Were Harmed: Nasty Jack's voice is based off of Jack Nicholson's, as are his name and even his physical attributes.
Not-So-Harmless Villain: Nasty Jack, introducing himself as a Visual Pun, is far from the most sinister or serious Pooh villain, but is the most competent, keeping one step ahead of Pooh's team the whole episode until Piglet prompts a Heel–Face Turn.
Shrouded in Myth: Nasty Jack. "He'll trounce you left and trounce you right and tap dance on your head!"
Some of My Best Friends Are X: Rabbit shouts, "Some of my best friends are horses!" as Nasty Jack attacks him at the saloon.
Suddenly Shouting: Rabbit, when Nasty Jack threatens him for putting a carrot on top of his banana split instead of a cherry.
Rabbit: Uh, let me answer that by saying, HEEEEEEEELP!!!!!!
Taught by Experience: Nasty Jack isn't amused when the Masked Bear gets the jump on him to save Piglet. So he fakes a distress call, traps the Masked Bear and his noble steed, and then challenges Piglet to a duel.
This Is Gonna Suck: Eeyore's reaction when he sees the horse thieves about to slam him and Pooh with barrels. He has the same reaction when he and the Masked Bear crash into the sheriff's office.