The trilogy holds a special place in my heart with regards to cinema. The musical scoring is fantastic, perfectly capturing the epic feeling of the narrative. The visuals are overall amazing. It came out just when making Jurassic Park* level digital special effects became cheap enough to include in many-to-most shots, but still expensive enough that practical effects like forced perspective for the hobbit sizes was still considered preferable. For this reason, I think they got the usage of digital effects right, not deferring to their use when another method would work. Likewise, it came out at the tail end of when most western-culture-produced movies only included women/bipoc actors when it was plot-relevant, otherwise defaulting to white men. For that reason, I give it more of a pass than if I saw it in something made today. With that in mind, the casting is very solid. Mortensen, Lee, Serkis, and Weavings' Aragorn, Saruman, Gollum, and Elrond are definitive versions in my mind (Weaving being the standout surprise, as I expected to see bits of Agent Smith poke through, but I did not). I could see other actors of the right ages playing Frodo, Sam, Boromir, and Gandalf, but I think Wood, Astin, Bean, and McKellen's interpretations were very powerful and I doubt another matchup would have done strictly better. The rest of the cast did fine to exceptional work, often depending on whether they were given much room to act (for instance Orlando Bloom got to look unfazable and badass as Legolas, and not much else), and even my biggest complaint -- Rhys-Davies bloviating clown Gimli was in fact a very good rendition of what he was undoubtedly asked to portray.
*And, much like Jurassic Park, the effects still hold up today, which other movies of the time (like The Phantom Menace) often do not.
To that point, there are places where I would do something different. Galadriel's 'if you gave me the ring' moment looks like someone loved their photonegative filter, Shelob's webbing looks like it was made out of rubber bands, the fortifications and battle strategies are strictly rule-of-cool, and such. Certainly there are places where the film deviates from the books, and I can understand if someone asks why there needed to be elves at Helm's Deep, why Faramir and Denethor received virtuousness downgrades, or why Gimli was made into comic relief. This later critique, however, I think requires acknowledging that some changes needed to be made to make the books viable as films* and also that the films were intended to be adaptations, not perfect mirrors of the novels*. Overall, there are certainly things I would have done differently**, but nothing I consider actively objectionable.
*certainly every 'how I would have done it' posting I've seen in the nerdosphere by someone angry with these decisions either would never have been a hit movie and/or makes other changes someone else would find equally objectionable.
**and yes, we all have different ideas about how much should be changed when adapting someone else's work. Cue 50-page Starship Troopers-Watchmen-Don Quixote/Man of La Mancha tangent.
***and that goes for the novels, too. They are masterpieces of their genre, but certainly not beyond reproach and critique.
Overall, I think the LotR films stand up and will continue to be seen as masterpieces. What will get lost, especially to people who started watching cinema after their release, will be how much a departure from the norm these films truly were, both in their execution and the simple fact of treating the fantasy genre as serious cinema and blockbuster material. I'll forever defend Beastmaster and Krull and such as exceptional for their era, but LotR might be the first (Excalibur and Clash of the Titans maybe getting honorary mentions) to be truly exceptional, full-stop.