"My name is Gregory Goyle and I smell." Written next to the entry on trolls for bonus points.
The book's intro talks about how wizardkind sought to differentiate between "beings" and "beasts", with the first classification of a "being" being anything that walks on two legs. This subsequently leads to chaos at a meeting of all these "beings": trolls smash the place up, hags look for children to eat, and Augureys make a huge din. Ultimately, the wizard in charge of opening the meeting runs cursing from the hall after slipping on some Porlock dung.
This conversation scrawled on the first page:
Harry: This book belongs to Harry Potter.
Ron: Shared by Ron Weasley because his fell apart.
Hermione: Why don't you buy a new one then?
Ron: Write on your own book, Hermione.
Hermione: You bought all those Dungbombs on Saturday, you could have bought a new book instead.
Ron: Dungbombs rule.
And of course Janus Thickey's "last words", a scribbled note saying:
The Niffler. When it escapes from Newt's suitcase into a bank, Newt tracks it down to a bank vault, wallowing among the contents of a safe deposit box ("Really?"). He scoops it up, and it gives him a cute look — then he turns it upside down and a small mountain of coins, jewels and gold bars falls out of its storage pouch. Then Newt tickles the Niffler to get more to fall out!
Later, when it's escaped again, he and Jacob find it pilfering trinkets in a jewelry shop, made even funnier when it tries to pose as adisplay dummy — followed by Newt making a face that screams "You Have Got to Be Kidding Me!" when he sees this. Newt proceeds to clamber all over the cases trying to retrieve it, smashing various articles, and at one point ends up swinging from the shop's chandelier. Meanwhile Jacob's waiting outside, getting more and more nervous as the noise level rises - and then one of the catches on Newt's suitcase flips open, and something within roars.Poor Jacob.
And then the cops show up. Jacob, covered with jewelry from the store the niffler was rummaging through, points down the street and says, "They went that way officer".
While Newt and Tina are at her desk in the Wand Permit Office, she hides behind her desk when Abernathy comes in asking her if she butted into another Investigative Team meeting. Even Newt is amused by this according to the screenplay.
When Newt and Jacob are in Tina and Queenie's apartment as the sisters prepare dinner, Newt's itching to leave and is heading for the door. Queenie curtails him by asking if he prefers pie or strudel. When he nervously says he doesn't have a preference, she turns to ask Jacob - who's already seated and tucking in a napkin, with an eager smile on his face.
This conversation between Tina and Queenie as they're setting the table, where Queenie learns what Tina had for lunch:
Queenie: Hotdog, again?
Tina: [annoyed] Don't read my mind.
Queenie: [disapprovingly] Not a very wholesome lunch...
The ending of the official teaser has Newt descend into his suitcase while Jacob watches with wide eyes, a mug halfway to his mouth. Then Newt whistles, his hand beckoning from the suitcase, and Jacob can only point at himself in bewilderment.
Even better in the movie itself: when Newt climbs into his suitcase, Jacob lets out a loud, shocked "PAHA!" before Newt calls him over.
Then as Jacob is getting in, he makes it about halfway before getting stuck and struggles to get himself the rest of the way in.
Kowalski's reaction to seeing all the magical weirdness around him and accepting it; "I ain't got the brains to make this up."
This exchange, if only for Newt's blunt way of saying it:
At the jewelry store, before the cops can apprehend Newt and his companions, a lion suddenly appears behind them, casually walking on the sidewalk.
Newt: You know, New York is considerably more interesting than I expected!
Another rather comical thing about this scene. Notice the weapons the cops are using. Each one has a shotgun. Thanks to that lion, we will never know if a muggle with a shotgun can defeat a wizard.
And then as Newt and Jacob arrive in Central Park, an ostrich runs past them. The confused noise that Jacob makes is priceless.
And then Newt hands Jacob a helmet to protect him from the Erumpent they're looking for.
Jacob: Why — why would I have to wear something like this?
Newt: Because your skull is susceptible to breakage under immense force.
And THEN he laces him into some body armor while telling him not to worry.
Jacob: Tell me, has anyone ever believed you when you told them not to worry?
Newt's bizarre mating dance to lure the Erumpent toward him and away from the hippo.
The Erumpent chasing Jacob across Central Park in an effort to mate with him. With a romantic score playing, to boot! And Jacob Screaming Like A Little Girl as he runs.
While Jacob deals with the Erumpent, a baboon steals Newt's wand, and he tries to get it back.
How does Newt get his wand back? He doesn't swipe it away himself, but the baboon begins smacking the wand into a rock business-end-first, and it randomly discharges, sending the ape flying into a pen.
Tina explains the escape of the magical creatures to the MACUSA, then sets a briefcase on the floor and knocks on it. Newt emerges, only visible from the chest up.
When Queenie and Jacob try to break into Graves' office, she tries different unlocking charms to no avail and doesn't know what to do. Then Jacob just kicks the door in...
On a meta level, Eduardo Lima, one of the graphic designers for this series as well as the Potter series, inserted the headline "No-Maj singer is a goblin" into one of the prop newspapers.
Newt objecting to Queenie naming Ilvermorny as the best magical school in the world, and defending Hogwarts' own claim.
Jacob: Is there a school, a wizardry school, here in America?
Queenie: Of course! Ilvermorny. It's only the best wizard school in the whole world!
Newt: I think you'll find the best wizarding school in the world is Hogwarts.
When Credence's Obscurus is rampaging around New York towards the end, Newt tries to go after him, giving his bag of magical creatures over to Tina to hold it for him before apparating off to find Credence. Tina holds it for a moment before handing it off to Queenie saying she needs to hold it so she can go after Newt. Then Queeniehands it over to Jacob and starts trying to go after Tinabefore Jacob stops her.
After days of his beasts escaping his suitcase and wreaking havoc, Newt finally secures the suitcase better so none of them can escape again. By tying it up with string.