I just sat down to watch the first couple episodes, and I kept notes throughout. Here are my thoughts, adaptation opinions, and predictions.
Episode 1
General thoughts
About three quarters of the way through E1 I decided that I don't think this show really counts as an adaptation of Tolkien's stories. I will be treating it, just when judging it generally, as a new story using some of Tolkien's characters, settings, and events. That being said, I do have opinions on its use of the source material, and will be sharing opinions on that below.
Notes, thoughts, and random musings
You will have to put up with my random musings forever. They are a natural part of my experiencing anything. Some are more important, some less.
The opening sequence was very counter to my imagination. There was still light after the Trees were gone. Also, the trees burned up sort of, instead of having the light suched out of them. The ships going to Middle-Earth intrigued me, but it's a one-off so I'm fine with it. The battle scene was also very cool.
Galadriel's whole arc rests on Finrod having died in pursuit of Sauron. This isn't wrong, per se, but it leaves out the very important circumstances of that death!
I very much liked the shot of Sauron during the opening.
Their torches gave off no warmth but still light?
Everyone should know what Sauron is; at least Galadriel will know he is a Maia. There seems to be a lot resting on the mystery of not just who, but what he is.
The captions had them speaking in Quenya. They would have used conversational Sindarin.
I like the Harfoot characters but I don't really like how they've treated them as a whole, since for all intents and purposes they're proto-Hobbits - I wouldn't be surprised if they chose Harfoots because it sounds the most like Hobbit, unlike Stoor or Fallohide.
Elrond was forbidden from an all Elf-Lord council. He is the son of Eärendil. It doesn't get much more lordly than that, unless they're discriminating against him because he's Half-Elven, which it doesn't seem.
Celeborn - where is he? [See predictions]
Elanor Brandyfoot is a name that should not exist yet. Elanor is a flower from Lórien, and to our knowledge Sam was the first to name his kid that. Brandy came from Brandywine.
Of all people, Elrond should be sympathetic to Galadriel. He's very somber, it's kind of a thing with him. He seems far too chipper here.
I honestly don't mind Arondir and Bronwyn's romance, which I expect to be controversial. The story of Mithrellas and Imrazôr indicates to me that Elf-Man romances are more common than just the three mentioned in the Silmarillion and LOTR.
Regarding that, Arondir's captain does say it has only happened twice before, and both times ended in death. I assume he is referring to Beren and Lúthien and Tuor and Idril. Technically they all did die at the end. But Tuor and Idril did not die in the fall of Gondolin, and Beren in fact got resurrected.
Arondir comments that he has not seen alfirin for a long time. The plant may not be native to Harad but it's common elsewhere - it's mentioned in Legolas's song of Lebennin and is also called simbelmynë - which we all know.
The name Hordern reminded me of Michael Hordern, who played Gandalf in the BBC Radio LOTR series.
Ents! There was a shot of Ents and I liked it.
I like the Harad story.
My other biggest qualm with this episode - their treatment of Valinor. The king has to give people the ability to return? And then there's a big choir and light when you get there? Where the heck are they getting this information? That seems totally wrong - and it's important too! This was the weirdest adaptation choice I think they made.
Adaptation opinions
I mentioned Valinor, but I feel they're kind of just taking names and concepts from the Silmarillion and putting them in without much concern for how they actually work. I first noticed this at the title sequence, but it carries generally.
On the characters: I actually really like this Galadriel. I think some people will think of her only through the sedentary Lady of Lórien, but I don't mind her as a warrior. But she's also looked down on a lot. Gil-galad and Elrond are both younger than she is, and both kind of lord over her. Gil-galad is the king, yes, but Elrond? Speaking of Gil-galad - I've always seen him as more like Finrod, though we don't know much about him. Here he seems rather too old and wisened. He did live through the Wars of the Jewels (depending which version you believe...) but aside from the "really wants peace to happen" side of him, I don't see much else I recognize.
On the story
Outside of the adaptation, I think this show does a pretty good job at storytelling. I don't think they'll worry too much about staying in the canon of the Silmarillion or even the appendices, but with regards to LOTR canon, I think they'll stay within their bounds.
Predictions after Episode 1
Galadriel and Celeborn will romance throughout one season. Not this one.
The Harfoots will reach the Shire by the end of the show.
There will be no Annatar. The name is a giveaway.
The Rings will finish their forging by the end of this season and (if what I've heard about their treatment of Númenor is correct) Tar-Palantír will die. S2 will cover the leadup to the War of the Elves and Sauron and the early kingship of Ar-Pharazôn. Then, broadly, S3 will be the War, S4 the Fall of Númenor, and S5 the War of the Last Alliance.
Episode 2
General thoughts
I liked most of this episode, though it seemed to drag at points.
Notes, thoughts, and random musings
I really loved the title sequence.
One of the Harfoots mentioned "the next three seasons" and I thought that was funny.
I didn't like Bronwyn calling an earthquake a ground-shake.
Eregion looked really nice - so did all the landscapes.
Celebrimbor and Elrond had no escort to Khazad-dûm.
Elrond calls Khazad-dûm Elmendéa. This sounds nice but does not seem to be supported - the Elvish names given are, according to Tolkien Gateway, Casarrondo (Q) and Hadhodrond (S).
Khazad-dûm seems to be too close inside the mountains, but is very pretty.
I was worried, with the horns on the plinths, that Sigin-tarâg would be a drinking contest. I am glad it was not. We do not need a scene from the films all over again.
The worm was weird and I didn't understand its significance except as a plot device and action piece.
Halbrand felt like it was a name that came from elsewhere.
The dwarf bits were cool.
I noticed that the incumbent king of Khazad-dûm was listed in the notes on Prime as Dúrin III. This should not be the case, as Dúrin IV should be a resurrection of Dúrin III, and that would be disproven pretty easily if they were alive at the same time.
Adaptation opinions
I didn't have a lot to say here, but I noticed it the title sequence it said "Based on The Lord of the Rings and Appendices", implying there was no license or input from the Silmarillion. I am not sure.
Predictions after Episode 2
The Stranger is a Maia but not Sauron. I suspect Olórin, Aiwendil, or some unnamed servant of Varda. He speaks the words Mana Úrë. I wonder if this is an attempt at Manwë, Aulë, or Ulmo. I cannot be sure.
I still think Annatar will not be named, but I do think Sauron will still influence Celebrimbor's forging process.
There will be a point at which Narvi makes the doors.
Some Haradrim will still become servants of Sauron.
We will see Númenor next episode.
And that's all from me! I will probably do this again next week for Episode 3.