Factual error: A theater marquee is visible promoting the showing of a film called Tribeca Follies. The acronym "Tribeca" - an amalgamation of "Triangle Below Canal [Street]" - didn't come into usage until the 1970s.
Factual error: In opening scene of of 1920s New York the Statue of Liberty is in view with the modern refurbished gold leaf torch, not the original iron and glass torch. Lady Liberty's torch was not replaced until October 8th, 1984.
Factual error: At one point, Newt Scamander says he found one of his beasts in Equatorial Guinea. That country only got that name after independence from Spain in 1968; back in 1926, when the movie is set, the place was known as Spanish Guinea.
Suggested correction: The Wizarding world is under different political authorities than the Muggle world, which sometimes means countries have different names or boundaries than for Muggles (Transylvania, for instance, still has a national Quidditch team in the 1990s according to the novel of Goblet of Fire, whereas in the Muggle world it was long since absorbed into Romania), so it's entirely possible that in the Wizarding world, Equatorial Guinea was an independent country in 1927.
Other mistake: When Newt gives Jacob a suitcase full of eggs, he bumps into him, apparently swapping suitcases. If you watch carefully, the suitcases don't actually switch.
Factual error: In the final scene in the bakery, there is a fire visible in the oven. In bakery ovens, there is no open fire in the oven, it is in a closed cabinet below. Bread and cake are not grilled. (02:03:55)
Character mistake: In her speech outside the bank, Mary Lou Barebone mentions "the wireless" as one of the wonders of modern technology, which is the British term. A New Yorker in 1926 would more likely use the Americanism "radio."
Possibly, but is it probable? Big difference between hearing someone else use it and using it oneself. Just as an example, if I ever were to travel to Britain, it would be an instinctive habit to use words like "elevator" instead of "lift", or "apartment" instead of "flat", simply because to me, as an American, that's what they're called.
Audio problem: When Newt, Tina, Queenie and Jacob are peeking at Dougal at the department store, Newt says to Jacob and Queenie, "You two, head that way." His lips don't move at all. (01:25:35)
Continuity mistake: After eating their meal they're sitting at the table talking with empty plates in front of them. As they continue to talk all the plates and flatware disappear.
Continuity mistake: During dinner at the Goldsteins', the dishes are empty from one shot to another.
Other mistake: A shot of Jacob and Queenie walking was used twice. Queenie is showed on the left side of the screen and Jacob on the right, and Jacob looks behind, then turns to look to his left, then turns more in front of himself. This happens while Queenie and Jacob are trying to find Newt's case, then find what cell Newt and Tina are in when they are trying not to be killed by Grindlewald in disguise.
Character mistake: Toward the end of the movie, the behavior of Newt is totally out of character - not just for him, but for any sane person. Newt tries to save Credence, and he has just gotten him to stop attacking and actually listening - when the other wizards blast what Newt knows to be essentially a traumatized and abused child to kingdom come. But Newt isn't the least bit distressed or mad, he just shrugs it off in a "shit happens, life goes on" kind of manner, catches Grindelwald for them and helps them save the world, happy as a flea and not giving a damn about the recent death of Credence. Only a complete and utter sociopath would be totally unmoved by the death of a child they were trying to save. A sane, feeling person (like Newt) should be at the president's throat spells blazing, cursing her and the whole American Wizard-hood to the nether regions of hell and not giving a blue damn whether or not they are exposed and in trouble, and whether or not Grindelwald goes free, because in that moment, in his eyes they would be hardly better than him. It is even more out of character since Newt is until that moment depicted as extremely protective of his creatures.
Suggested correction: Newt certainly does show sorrow for not being able to save Credence, but you are putting too much on Newt. Through the whole movie we are shown and told multiple times that Tina is the one close to Credence. She is the one who saved him once before and lost her job for it. Newt is a stranger and tries to help. And also not a powerful enough wizard enough to start fighting the President and her aurors. You decide he shows no emotion which he does, but at the end of the day he is not the one with closest connection to Credence.
Yes, he does show sorrow (which I never claimed he didn't), but only for a moment, and not nearly as much as say he earlier showed when his suitcase, containing mere animals, was taken from him. His reaction neither feels natural nor would be considered normal in a psychological review. Also you completely overlook the fact that newt is close to Tina, and come to think of it, her reaction is hardly normal either considering her history with Newt. Yes, admittedly I drew a rather colorful picture of a possible reaction newt might show, "spells blazing" is probably a bit on the extreme side. He'd probably rather tell her to go to hell and solve her own problems though instead of being eager to help.
