Tolkien wrote comparatively little on the Second Age, so entire story is a bare-bones outline that it seems that someone could easily use to work within. But Amazon has taken a lot of substantial liberties with the stories. It make sense that a lot has to be added, because there's not much to go on, but quite a lot has been changed, with the "actual" occurences being treated more along the lines of call-backs or nods-and-winks.
Firstly, the biggest and most obvious change is that the entire story has been compressed dramatically. In the Appendices to the Lord of the Rings, the primary source material used very loosely in the show, here is the outline of events, up to the last thing that has occurred in the show:
c 500 SA. Sauron begins to stir in Middle-Earth.
c 1000 SA. Sauron makes Mordor his stronghold and begins building Barad-dur.
1200 SA. Sauron begins working with the smiths of Eregion.
c 1500 SA. The Elves and Sauron begin forging the Rings of Power - this must mean the 7 and the 9.
c 1590 SA. Celebrimbor completes the Three.
c 1600 SA. Sauron completes the One Ring, and Barad-dur. The War between the Elves and Sauron almost immediately begins.
1699 SA. Sauron overruns all of Eriador after destroying Eregion and killing Celebimbor.
1700 SA. Tar-Ministatir sends naval expedition to relieve Lindon. In the following centuries, the Numenoreans establish colonies and 'dominions' on the coasts. Sauron focuses on the East, but still rules much of Eriador.
2251 SA. The Nazgul first appear.
~3175-3255 SA. The 'repentance' of Tar-Palantir from the increasingly bad behavior of the Numenoreans; civil war in Numenor referenced in the show; Miriel and Ar-Pharazon.
In the show, we can clearly see at least 2200 years of events have been condensed into at most a few months. None of the Numenorean characters on the show would be born for more than a thousand years when Celebrimbor made the Three.
Secondly, another substantial change is the treatment of the Fading of the Elves. Clearly, this did make its way into the show...as an entirely separate idea, the concept that "corruption" in Middle Earth killing their tree will soon extinguish the Light of Valinor in them and force them to flee Middle-Earth. Strangely, Elves that never visited Valinor seem to be under the same affliction, and Gil-Galad is treated as the High King of all the Elves, and not only the Noldor - other Elves seem to hardly exist. This ties into the strange plotline where mithril is given all sorts of magical properties it does not have in the books and to have been formed as a result of a magical conflict between an Elf and a Balrog, which it was not. In short, the Fading was not an imminent disaster facing all living Elves - there was no reason most of them had to leave ME in the Second Age.
Thirdly, a lot of characters are busy doing things in the show that they should not have been doing, or that don't make a lot of sense. As the chief example, Galadriel missed out on the War of Wrath, because she and Celeborn
left Beleirand before the Fall of Nargothrond. In the Second Age, Galadriel and Celeborn were busy having their daughter, and were regarded as the Lord and Lady of Eriador, and they founded (!) Eregion. But by the time of the forging of the Rings, Galadriel and Celeborn were already dwelling in (what was later called) Lothlorien. She was certainly not wandering around the North looking for Sauron, because she already felt that whatever evil was in Middle-Earth came from the east.
There are lots and lots of other little odds and ends that have a substantial impact on the story. For example, the palantir could not see the future. This is a major and unnecessary change (why can't Miriel just dream it?), and a King of Numenor would be in absolutely no danger from the use of a palantir. Or consider that in the original timeline, the Three Rings were the culmination of the Elves' Ring-work, where in the series, they were the first Rings made, no prior "essays in the craft" of lesser Rings or Great Rings necessary. Similarly, by the timeline of the Lord of the Rings that the show supposedly uses as its main reference, the Istari do not arrive until later in the Third Age (later writings have two arrive in the Second Age, but still by ship), and certainly not Gandalf, and they arrive by ship and in control of their faculties and not on meteors. It is not clear to me why the cultists think Maiar should be confused: I presume this is drawn from Gandalf the White's condition, but his is a very special case and not at all true for Ainur in general.
There are also truly minor quibbles - people seem very upset about dwarven women, which are supposed to be indistinguishable from the men (to outsiders), and it seems hardly likely that anyone would describe Miriel as fairer than silver or ivory or pearls.
In sum, the Rings of Power should be seen as only very loosely based on Tolkien. One could hardly expect it to be faithful to the spirit of Tolkien in this era, but even the narrative details are a loose guide at best.
