The key is what they change and how. On Game of Thrones, there were lots of changes that didn't look like a big deal, but turned out to have serious implications. Some of it was the characterization of Ned Stark, how they dumbed him down and made him a simple warrior, who didn't understand politics and leadership. Ostensibly that doesn't seem important since he dies in book/season 1, but what it showed was they had no understanding of the setting or how the politics work, because they don't appreciate all the subtle strengths of Ned's leadership. In the books, long after his death, people are still rallying to his cause in his name and his memory and the kids he raised are, or will, hold to his example which will give them the ability to save the world or pick up the pieces again. But the showrunners only saw that he got killed, so he "lost" the "game". And the exact inverse applies with their portrayal of Tywin, which lead to the completely nonsensical politics of the later seasons and the forced and arbitrary conflicts and idiot plots where characters did illogical things to set up changes of fortune to keep conflicts going that should have instantly been settled. They cut out a seemingly minor character who only appears in the last published book and only in a handful of chapters, so it does not seem like a huge omission, until seasons 7 & 8, when it seems clear he is supposed to take the place of Cersei as the main political opposition. By cutting him and leaving Cersei in, they were seemingly engaging in narrative economy, except Cersei was no longer credible as a threat or political opponent, so they had to totally shred the good guys' forces with implausible defeats and moronic strategies that left them in positions of weakness, in order to keep Cersei in the game.

So we can't necessarily say which changes on screen will be acceptable and necessary trimming and which ones will escalate into massive problems and which ones might not be a big deal, but demonstrate a lack of understanding of the source material that will lead to losing more incompetent handling of critical story points and character developments.

Yes.

Stuff like that. Lots of fans might not care about the mechanics of the One Power, but keeping them consistent, especially for a fantastic element to the story of the author's invention, is important to maintaining the verisimilitude of the plot. If one sister can hold Logain, it either Worfs him or raises questions later on about the limitations of Moiraine or Rand's ability to beat other sisters.

It's like the fight scene they show with Moiraine & Lan at the end that looks like they are defending Emond's Field from the Trollocs, but Moiraine calling down a lightning storm. Nothing WRONG with that and it looks cool, but for Moiraine to singlehandedly save the village (instead of just a lot of individual lives and that as much with her Healing as her lighting or fireballs) undercuts the Two Rivers folk and at the same time exceeds her own limits. If she can save the village, why do they spend the whole book in her company running and hiding? Why do they have to take the incredibly dangerous Ways out of Caemlyn? Even if there are more Trollocs around Caemlyn, there are many more sisters in the city, not to mention a significant military presence. Why can't Moiraine and the sisters there with Logain defend the city from the Trollocs gathering in the countryside? Because the reality is, Moiraine was not that powerful, she could handle a couple of Trollocs in a skirmish, but she's not a WMD.

I think you are referencing a line from tDR, in Illian after the Grey Men attack, and Perrin says out loud that Rand is the Dragon Reborn, not him. Moiraine then tells Faile that there's no going back for her, she's going to come along and cooperate, or die, because she can't be trusted running loose with this information. No one knew about Rand in EotW or tGH to tell.

I didn't either, and started to comment on it, but then there is the thing that comes up later in the series, where the Aes Sedai actually use gestures and it is explicitly stated to slow them down. Sorilea scoffs to Cadsuane about "all the hand waving you Aes Sedai do" in tPoD, and when the Seanchan arrive after using the Bowl of the Winds, Elayne notices that the Windfinders and Aviendha have a higher rate of fire than the sisters, because they don't use gestures, so there is no physical limitation to how fast they can produce new missiles, while Elayne, Nynaeve, Sareitha, Careane, Vandene and Adealas all have to wind their arms back and swing them forward for each one they loose.

So the gestures, even if not necessary, are a thing they do and thus we actually get a visual representation of how it slows them down. This, I believe, is one of the potential greater advantages of the medium, especially if they pay it off when the Aiel & Sea Folk take a bigger role.