The Appendices basically contain the Cliff Notes version of the events prior to the Third Age, including the sinking of Numenor, but the bulk of it, and the more detailed version of it, are set out in The Silmarillion, The Unfinished Tales, Children of Hurin, Fall of Gondolin etc... which Amazon do not have the rights to. That's why in the trailers it says that it's "Based on" the works of Tolkien rather than "Adapted from". So because of that, from what we've seen in the trailer, teasers, interviews etc., what we will see in The Rings of Power will greatly diverge from Tolkien's lore, e.g.;
Numenor being ruled by Queen Tar-Miriel with her husband Ar-Pharazon as her advisor. In Tolkien's lore, while Miriel was the heir apparent, Ar-Pharazon forced her to marry him and he usurped the throne becoming King. It was he who later "captured" Sauron (after he discarded the Annnatar persona), and it was Pharazon who, after Sauron became his chief adviser, decided to attack Valinor.
In Tolkien's lore, Galadriel at this time was already married to Celeborn and they moved from Lindon to Eriador before finally settling down in Lothlorien. In RoP, Galadriel appears to be unmarried - Celeborn doesn't appear to be part of the show. And she is now a warrior, leading armies and slaying orcs - totally different from Tolkien's lore.
Galadriel never went to Numenor and never met Tar-Miriel. But in the show, from the trailer with the palantir, it seems both of them are working together, and are the ones that sensed the coming of evil - in the lore, it was Galadriel, Elrond and Gil-galad that afsensed Annatar wasn't who he said he was.
And I really hope that Eminem looking fella isn't Annatar. In my mind, Annatar should look like Lee Pace as Thranduil in The Hobbit.
The show supposedly has King Durin III and Prince Durin IV at the same time. In Tolkien's lore, the Dwarf kings are named Durin because they are believed to be reincarnations of the Durin that came before. So having two Durins at the same time doesn't make sense.
That Balrog that appeared at the end of the trailer better be a First Age flashback. After the War of Wrath, there is no mention of any Balrog throughout the Second Age until Durin's Bane in the Third Age.
But probably the biggest beef with Tolkien fans is the time compression: the rise of Sauron (as Annatar), the forging of the rings and the reign of Pharazon to the fall of Numenor take place over the course of about 2000 years. In the show it looks to be compressed to just over a few years to fill out the proposed 5 seasons.
With all these changes its no wonder Tolkien purists are up in arms with regards to this show, as it greatly changes Tolkien's lore. In fact, there's a rumor going around that Tom Shippey, the Tolkien scholar that was advising on this show, was actually fired because he told the showrunners that they were polluting the lore.
Perhaps the only shot I like in the trailer was that with the Two Trees of Valinor - truly gorgeous. But I'm not holding my breath for this show to be good. The fact that it will be released on the anniversary of Tolkien's death is kind of disrespectful for me, exacerbated by the "the past is dead" line in the trailer.