These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Animation Age Ghetto: Siskel And Ebert's complaint about the movie was that it was too dark and depressing for children to handle. They said much the same thing about every Don Bluth movie though. The box office money it made shows that kids and adults were watching it anyway.
First Installment Wins: Though there was a stretch during the nineties where Fievel Goes West was equally well-known, due to being a decent film with a simple genre hook, and also a spin-off series to keep it in kids' minds. Since then it's slipped back below the original in terms of popularity.
The movie is sometimes mistakenly called "Fievel" - that the sequel does have Fievel's name in the title likely doesn't help.
Interestingly, in most other countries Fievel's name is in the title. Take Germany's Feivel Der Mauswanderer (Fievel The Mouse Wanderer), Spain's Fievel Y El Nuevo Mundo or French's Fievel et le Nouveau Monde (Fievel And The New World), for instance.
Misaimed Marketing: Infamously, if unintentionally (one would hope), done by McDonald's. One of their special promotions tied into the film's winter release was a special offer involving Fievel... Christmas stockings.
Narm Charm: Fievel and Tanya singing "Somewhere Out There", with their little mouse voices cracking when they hit the high notes. To some it might be annoying, but to others, it's so cuuute!
Nightmare Fuel: The Russian cats that act more like Slasher Smile mouse exterminating monsters incapable of speech when compared to the gang like but less threatening New York Cats.
The Giant Mouse of Minsz created by the mice is scary looking, not helped that it was rotoscoped to contrast with the rest of the scene.
When Fievel is sold into slavery.
The wave that takes a demonic form before taking Fievel off the boat
The Woobie: Fievel. Your mileage probably won't vary much.
Jerkass Woobie: The three orphan bullies, if you stop and think about it.
Fievel Goes West and Fievel's American Tails
Angst? What Angst?: Fievel's parents really don't seem sad or concerned enough when Fievel falls off the train, and when they get to Green River they're more concerned about where they're going to be living than the whereabouts of their son. And when Fievel is reunited with them, they're happy, but they don't make a big deal out of it, as if it were some daily occurance. Considering they already declared him dead in the first film, you have to wonder what kind of parents they are.
Fans have debated the canon status of this film for quite some time. The third movie seems to imply that it was All Just a Dream, but it's vague enough that it can be interpreted as a mere shout-out.
A third group of fans also see it as non-canon, not because of the dream but because Don Bluth was not involved. These fans often forget that Steven Spielberg and David Kirschner had much more to do with creating the story than Bluth did, who for the most part just handled the animation side of things, Kirschner having come up with the initial idea of An American Tail. Bluth nonetheless was responsible for the first movie's gloomier atmosphere.
Idiot Plot: Cat R. Waul being the Big Bad of the TV series means almost every episode requires every character except Fievel to fall for his latest scheme.
Memetic Molester: From Fievel's American Tails, there's Dr. Travis T. Hippocrates, a traveling doctor who encourages Fievel to give strange candy to everyone in Green River (which ends up giving everyone hiccups, and he sells them a placebo "cure"). Fievel doesn't think twice about taking candy from a stranger. Later on when Fievel refuses to be a part of his scheme anymore, he grabs Fievel by the shoulders very suggestively and says "Fievel, my boy, I'm afraid that was the wrong answer.", and the scene fades to black.
The Problem with Licensed Games: The Fievel Goes West game for the Super Nintendo Entertainment System wasn't too bad of a side-scroller, but it wasn't too impressive either. In the early 2000's Fievel even got a game on the Game Boy Advance, An American Tail: Fievel's Gold Rush, which seemed to take place after Fievel Goes West and played a lot like the Super Nintendo game (odd given that Universal had spent so much effort trying to convince everyone that the movie never happened). This trope is played far more straight with the random An American Tail game that came out for the PlayStation 2in Europe (which actually plays disturbingly a lot like Superman 64).
Sequel Displacement: When it first came out and for a few years after, though it's slowly gone away.
The Direct-to-Video Sequels
Anvilicious: The Treasure of Manhattan Island and its constant reminders that the Europeans did some pretty awful things to the Native Americans. Granted, Some Anvils Need to Be Dropped, but it tends to go a little out of its way to do so at times.
Bizarro Episode: The fourth movie, The Mystery of the Night Monster, really doesn't have anything to do with the rest of the series. While the third movie at least made a few allusions to the first movie, the fourth one is just kind of all by itself canonically. At worst it seems like a recycled plot for a Scooby-Doo movie.
It was created at the same time Universal was producing two "spooky" themed Alvin and the ChipmunksDirect-to-Video movies, so it would seem The Mystery of the Night Monster was part of some spooky phase their animation studio was going through.
Contested Sequel: Though most fans agree that both films don't stand up to the first two movies, there is still disagreement over which of the direct-to-video movies is better than the other.
Judging by forums, the 3rd is much preferred over the fourth.
Madame Mousey herself, and to a lesser extent Nellie Brie, both also have a strangely sizable amount of fan work devoted to them.
Fanon: There are fan theories which link the direct to video sequels to Fievel Goes West, and several different explanations for why Bridget didn't appear in the 3rd or 4th movies but is seen with Tony in the 2nd (which would have to have happened after the 3rd and 4th movie chronologically for them all to be canon).
Fanon Discontinuity: For a lot of fans (especially if they really liked Fievel Goes West, due to the 3rd film proclaiming it to be All Just a Dream) these movies never happened. On the other hand, the 3rd film is remembered by fans of TMS Entertainment at least.
Meanwhile, the above Fanon is usually followed with the understanding that the creators of the third movie probably wanted to RetconFievel Goes West. It's just more fun to disregard that and try to make sense of the jumbled continuity themselves.
Only The Creator Does It Right: Tends to be the opinion of most fans when it comes to the direct-to-video sequels (as well as those who dislike Fievel Goes West due to Bluth's lack of involvement). Then again, compared to other Bluth sequels they could have been a lot worse.