The trainers worked just fine for me and I bought the game the day it was released. How can you train your skills wrong when everything in the game is statically leveled? All you have to do is make sure to build endurance enough to gain hit points and intelligence to gain mana, both of which could be done at the same time unlike with Skyrim where you actually have to choose one or the other.
Off the top of my head; the medium armor master training in the Tel Fyr docks did not have training dialogue, nor did the Armorer master trainer in Ebonheart. The Enchantment master trainer in one of the dumner fortresses was actually hostile to you while the less capable altmer next to him would offer you training up to ~50, thats not to mention the other master trainers that required guild memberships to access.
As for doing it wrong, you stole everything in vivec when you could just pick up the two swords of white woe in Balmora and Suran, make custom spells for drain >insert skill< -100 for 2 seconds and train everything up to 100 for 1gp per level, conveniently by-passing the problem of not all master trainers working properly.