Was out of town this weekend when this released, so I'm catching up now... or trying to anyway. The sheer amount of things they've changed dramatically compared to the source material in the first 20 minutes of the first episode is dumb founding.
Claiming that the Elves (specifically the Noldor) sailed from the Undying Lands to chase Morgoth has some kernels of truth to it, but it certainly wasn't because he killed the trees. It was because he, after killing the trees, stole the Silmarils from Feanor's vault. This change in motivation is
massive for the Noldor, who in the books committed the first act of "Kin Slaying" (killing other elves) to steal their ships (of which, Galadriel witnessed but did not take part), and their oath (The Oath of Feanor) to reclaim the Silmarils and not allow them to fall into
anyone else's hands would be a source of much of the drama and contention of the first age. Moreover, Galadriel and her brother (Finrod) did not take that oath, and followed not by ship, but by crossing the Helcaraxe (an area far colder and far harsher than Forodwaith). Galadriel journeyed to Middle Earth not out of some desire for revenge, but out of her desire to see Middle Earth.
Her brother, Finrod, was indeed slain by Sauron. But Finrod never vowed any oaths against Sauron nor did he specifically seek Sauron out. And, in fact, he was killed by Sauron well before Morgoth was ever defeated (while Sauron was still just Morgoth's most trusted lieutenant). He was slain during one of the most beloved tales of Tolkein fandom, the tale of Beren and Luthien -
which is specifically mentioned even in the Peter Jackson films - and is again related to both the Silmarils and the Oath of Feanor. Finrod is among those with Beren as he attempts to claim a steal a Silmaril from Morgoth in order to win the approval of Luthien's father, and when the party is discovered by Sauron, they are imprisoned and attacked by werewolves in Sauron's dungeons. Finrod saves Beren, but dies of his wounds suffered in the fight against a werewolf. Why the producers of this show felt the need to re-write Finrod's death makes no sense to me, as their desire for Galadriel's anti-Sauron motivation could still be left intact with the actual story of Finrod's death AND we know that the tale of Beren and Luthien is not off-limits because it was also alluded to in the Peter Jackson films. Why make this change?
Even the geography presented in the episode is wrong. Forodwaith is not some far far northern area that is never crossed by elves. Forodwaith is barely north of Arnor (the area where Aragorn was a ranger in while he was known as Strider and one of the kingdoms that he reunites as king), and not even that much further north than The Shire. It's about as far north as the Lonely Mountain. Galadriel spent much of the First Age in Finrod's kingdom of Nargothrond, which was further north than Forodwaith. It's certainly nowhere near as cold or harsh as the Helcaraxe, which she crossed after the Kinslaying. Why make the claim that it is some unreachable frozen wasteland far beyond where Elves typically journey when we know that to be untrue even after the destruction of Beleriand? Especially considering that Angband (or Utumno) are both further north and would make an equally valid target for their narrative purpose.
(Note - this map is not entirely canon and is attempt to show as much of Arda through all three ages as possible - much of it changes over the course of those ages as Numenor rises and sinks, Beleriand is sunk, and the Undying Lands are removed from the sphere of Arda when it is made round - but none of this changes the point I'm making)
edit - And they're changing the relationship between Galadriel and Elrond, just as I feared. Galadriel is his mother-in-law and a princess of the Noldor. Ugh.