I've watched this movie 3 times since its premiere on 16th November so here's some of my theories and speculations.
1) The real reason Newt came to New York is because Albus personally asked him to find Grindewald and maybe to study the Obscurus-linked incidents.
- The Minister of Magic asked Newt if his reason coming to New York is really to get an Appaloosa Puffskein. Newt also told Jacob that the reason he came to America is to release Frank the Thunderbird in Arizona.
2) Albus gonna asked Newt to Obliviate him using Swooping Evil potion
- Obliviate seems to be the central theme of the movie and it even introduce Swooping Evil as the source for powerful Obliviate potion. I think Albus gonna asked Newt to Obliviate him using that potion so that he would forget the death of Ariana and the betrayal of Grindewald and that's also the reason why Albus always talked in riddles during HP period.
2) Newt is studying Obscurus because Albus asked him. Ariana is likely an Obscurus. Obscurus might also be the key to the origin of Voldemort and how he split his soul into 7 parts.
- We didn't see what happen to Modesty or Chastity, Credence's foster siblings, either of them is likely to be the candidate to host the stolen Obscurus. Grindewald is hiding the Obscurus that Newt got from Sudan. Dunno if Credence really die in the end. Grindewald said "Will we die just a little?"
3) Queenie, a Legillimens is likely to be connected to Salazar Slytherin and Voldemort.
- Or maybe Luna Lovegood because she acts like one.
5) The Niffler might be hiding important Horcrux candidate in his cute nest.
- Because he's into shiny things!
6) Douglas the Demiguise might led us to the revelation of Invisibility Cloak.
- According to the textbook, Demiguise pelts maybe spun to Invisibility Cloaks. Demiguise has invisibility and some sort of divination and probably gonna have some important roles in the next movie.
7) Other observations:
- The symbol that Grindewald gave to Credence is the symbol of the Deathly Hallows - Elder Wand, Sorcerer's Stone and Invisibility Cloak.
- Some foreshadowing stuff that will puzzled the audience when they first watch the movie that only the screenplay writer know such as why would Newt asked Jacob and Queenie not to be predictable when trying to catch Douglas (because he can has some sort of prediction sighting), why Newt's wand permit application was not processed (because it turned into origami rat & fight with other origami rat), when Jacob opened Newt's suitcase the people on the street saw a hippopotamus (it's the Erumpent), why Newt asked Jacob to wear headgear and vest (Erumpent again), why Newt doesn't realized one of the Occamy missing (because one hatched during the bank scene). the Giggle Water was introduced in the opening scene after Grindewald attack.
- We're gonna meet young Albus, Aberforth & Ariana in the next movie.
- The sultry jazz song "Blind Pig" during the scene with Gnarlak is penned by JK Rowling herself. I love it!