The Gravity Falls bumper card: it's Dipper driving away from the gnome golem in the Mystery Shack golf cart (as in the pilot) and then crashing through a Welcome to Gravity Falls billboard, forming a silhouette in the shape of the Disney Channel logo.
In another bumper, when Mabel is choosing a sweater to wear she cycles through NINE that she was already wearing before choosing one. Who wears that many sweaters at once?
A third bumper has Stan receive a gold chain in the mail with the channel's logo on it.
In one TV short, Fixin' It With Soos, Soos modifies the Mystery Shack's golf cart so it can not only jump over Stan's car...but flies right into the Mystery Shack's roof!
During the car chase, one of the gnomes attacks Dipper, so Dipper lifts the gnome and smash him against the driver wheel again and again, and throws him outside the car, all while having an expression of annoyance.
The Legend of the Gobblewonker
Dipper saving Mabel from a falling tree—while they're still running away from the Gobblewonker! They just keep rolling and hit the ground running without missing a beat.
Something has to be said for Soos' (and later Mabel's) boat driving skills. At one point, Soos ends up driving the boat backwards while the Gobblewonker is chasing after them.
Dipper willingly going to fight the Multibear is pretty dang brave of him, considering he's the mortal enemy of beasts that are basically strength incarnate...
...and during the fight, he actually had the upper hand. He physically took down such a massive creature on his own...
...but him actually refusing to kill him after actually meeting the bear, not because it's difficult or scary, but because it's not the right thing to do, was even better. This kid stood up for himself in front of a man-bull the size of a small building.
Dipper: Hey, Pacifica, Nathaniel Northwest didn't found Gravity Falls, and your whole family is a sham. Deal with it.
A minor one, but when Grunkle Stan is put in the stocks, Pacifica offers to let him out if he agrees that her family is better than Mabel's. In writing. Stan agrees, but when Pacifica checks the notepad, it says "YOU STINK!"
Stan: Haha! I did that with my mouth!
Dipper, after having gotten his ass utterly kicked by the invincible video game character, has Robbie coming up to him ready to fight... and Dipper just tells him to go ahead and do his worst, which makes Robbie stand down. Dipper has faced far too much shit to let this guy scare him anymore at this point, and it freaks Robbie right out. Pretty damn well done.
Although misguided, you have to admit that Rumble Mcskirmish is Crazy Awesome.
Then there's Dipper deciding to face Rumble. He knows he has no chance, but there's no way out. As Soos put it, "Like a man it is."
Stan getting one over Gideon when he tries to scam into signing over the Mystery Shack to him.
Gideon: Stanford, you fool! You just signed the shack over to lil' old me!
Stan: Uh, you might wanna take another look there.
Gideon: The Mystery Shack is hereby signed over to... "suck a lemon little man"!?
Soos' Big Damn Heroes moment where he runs over the trickster with his pick-up truck.
During the fight with the trickster, Grenda manages to cut one of his forearms off with nothing more than a toy axe.
"I ate a man alive tonight."
Though they do little to faze the two children who are used to watching horror movies, the tricks Stan uses in attempt to scare them away were pretty cool. And he does finally succeed in scaring them at the end when they catch him half naked.
When Mabel starts taking charge. Its pretty impressive to see her boss around Wendy and Soos.
The fact that Dipper somehow managed to catch the Gremoblin.
Dipper turning the monster's OWN worst fear-inducing Death Glare against it.
Crazy an idea as it was, it looked like Stan was actually succeeding in giving that bear driving lessons.
The Deep End
Dipper saving Mermando's life by giving him reverse CRR, despite how unpleasant and unnecessary it was for him to do so. Seems he was cut out for the job of a junior lifeguard after all.
Dipper reveals to Wendy that Robbie's song has subliminal messaging to brainwash Wendy. This—and the fact that Robbie stated that he ripped the song from another band—causes Wendy to break up with him. Even better? Dipper wouldn't have found that out if Robbie didn't open his big mouth to say "Catch you on the rewind", which was exactly how Dipper found out about the message!
Not to mention that Grunkle Stan is the one that's helping Dipper out. As he states: "Road safety laws: PREPARE TO BE IGNORED!!!"
Soos figuring out that the baby pterodactyl's eyes are too far apart for it to see right in front of it, and escaping by having he, Dipper and Mabel walk in a straight line in front of its nose.
Soos pounding the geyser to launch himself and the Pines' back to the surface.
Old Man McGucket eating his way through a dinosaur.
Stan discovers Gideon broke in, and shoos him off with a broom.
A few flashbacks to Stan's life show him as a weak, bullied kid who learned how to box, take down kids bigger than him, and foil a robbery. Probably why he could take the pterodactyl.
Using the power of Imagination to take down a furious Bill. From lasers, to Kitten fists, to laser question marks, to synth music.
Then, they combine their powers to throw Bill out of Stan's mind and... Bill ends the fight by teleporting them all to a white space, Heroic Second Wind or no, he's still more powerful than them. He proceeds to calm down, compliment them, and deliver a cryptic warning before leaving.
Gideon just blows a hole into the shack and destroys the safe, beating them and having his dad take a wrecking ball to the shack.
Gideon: Oh, I'm sorry, Pines Family, did I wake you?
The fact that summoning a demon was his Plan A and that dynamite was his Plan B tells you a lot about him.
The "resurrection" of Xyler and Craz, and they're given quite an upgrade.
Dipper vs. Gideon in the giant Gideon robot.
To elaborate, Dipper took a running jump off the cliff, crashed straight through the Gideon robot's eye and tackled Gideon down in one smooth, continuous motion.
Dipper giving Gideon the beating he deserved.
Which included Dipper catching Gideon's fist during their fight, then twisting his hand around to punch Gideon with his own fist.
Stan exposing Gideon as a fraud and turning the whole town against him. He did this by realizing that his hearing aid is picking up some sort of feedback!
The shot of Gideon getting arrested.
"Here we go."
"Gravity Falls will return." With the way that line is said, it could mean a completely different thing than just the show.
The ending scene. The music is epic, powerful, maybe even a little scary—but it's also inspiring. Why? Because you, as the viewer, are witnessing the pinnacle of Stan's life. Stan has all three journals and uses the combine images in them to activate the machine. The way the machine lights up and he smiles, just like anyone who's just accomplished a lifelong goal would... it's truly, tearjerkingly beautiful. And the best part is, this is just the tip of the iceberg. We still have so much to learn...
Stan: Here we go. (cut to black)
Kinda makes you wonder why he would ever think "Is this all there really is?" when he's clearly had a powerful purpose for many years.
Fridge Sadness in that Stan is getting to the end of his life, and had spent years searching for the journals. The possibility that he could die without ever fulfilling that purpose would have to have gotten to him at times.
Brad Breeck (the composer of the soundtrack) is apparently working with Disney to get a Season 1 soundtrack released. In all likelihood, we're going to get the song from when Stan activates the machine on it.
Agents Powers and Trigger surviving the horde after getting dragged off into the woods.
Also, apparently, in this Universe, Ron Swanson is a government agent for a secret, paranormal investigating agency.
Into the Bunker
While all the group all does well, special mention goes to Wendy. Beforehand, it was unknown how well she'd do or if she would even go (considering the events of The Inconviencing, not to mention when she encountered Waddles in Soos' body, her avoidance in these events is justified). She proves herself to be awesome at this sort of thing. First, she spots the branch on the metal tree that opens up the titular bunker as well as climbing up to do so, Lumberjack-style. She then manages to find the doorway leading deeper into the Author's secret laboratories. She THEN manages to deduce that the "Author" of the journals wasn't who he claimed by seeing his picture on a can of beans, alerting Dipper. She THEN manages to hold her own against the "Author," really a shapeshifting creature known as Experiment 210, several times afterwards, the last time long enough reclaim Journal 3 from him (210 took it in an earlier struggle) and remove him as a threat to the group.
Wendy: It took us into it's home, tricked us and tried to destroy us. I'd say we return the favor.
Experiment 210 is a villanious one who proves to be more frightening than even Bill Cipher at times.
Pretty much everything after Mabel zip lines to Pacifica, which includes the two mowing through homicidal Lilliputtins, and a car chase that involves giant axes and a volcano.
The fight between Mabel and Bill Cipher. Especially so because Bill was pretty much responsible for his downfall because of all the abuse he put Dipper's body through compounding on the sleep deprivation Dipper had put himself through before the takeover.
Also, the fact that Mabel managed to put together a pretty fantastic puppet show with lights, original music, and full sets, and put it up at a local theatre, on a shoestring budget and with less than a week's worth of prep time. That takes some moxie.