These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
They don't constantly plot the destruction of the earth, they eat (with very poor table manners) and have their own hobbies; and anyone (with a Middle Ages mindset) would try to prevent their own demise even if they weren't completely accurate on it.
Complete Monster: SkekTek the Scientist is probably the most cruel and evil of all the Skeksis, seeing as his career is built around draining captured Podlings of their vital essence, reducing them to lifeless slaves. He then gives the essence - in liquid form - to the Emperor to drink and restore his youth... only briefly. Plus whatever experiments he keeps all the animals in his lab for. Word of God says that he alone fell the lowest of all the Skekses, perverting for his own ends the knowledge of the life of Thra he gained from Aughra while he was still an UrSkek.
Cult Classic: Reviewers have said that this is a visually stimulating film, but is one of Jim Henson's most underrated works.
Fridge Brilliance: The scene where the Chamberlain tries to convince Jen and Kira to make peace makes a lot more sense in the original version where the Skeksis had their own language. He's not speaking in short phrases to sound like he's dumb, he's trying to speak in broken Gelfling.
Fridge Horror: Those Landstriders they summon for transport, who later die fighting off the Garthim? Their cubs are left behind, presumably to fend for themselves.
What the Scientist does to those poor animals.
More of Fridge Sadness, since the Mystics and Skeksis are the same being, when you consider the posthumous Mystics probably died due to their counterparts Skeksis being killed off in petty schemes or battles with the Geflings.
Fridge Logic: In the Crystal Chamber, why didn't Jen and Kira sneak to each other once they saw each other, give Kira the shard so that she could fly on the Dark Crystal?
Why couldn't Jen have taken all three of the shards he'd identified as likely candidates, figuring out which one was needed later, rather than stick around trying to choose just one? Aughra didn't have any apparent use for the others, and the Garthem might not have trashed her place or taken her prisoner if Jen had already moved on when they arrived.
Nightmare Fuel: The scene where the Podling is drained... this troper couldn't sleep for weeks.
Fortunately, the Crystal being healed reverted all the drained Podlings. Hooray for Happy Endings!
Nostalgia Filter: Many a reviewer on Netflix admits that it hasn't exactly stood the test of time. Some even regret ruining their fond memories and wish they had never rewatched it.
Squick: The Chamberlain near the beginning gives us a glimpse of what a Skeksis looks like completely naked. It's not pretty.
Uncanny Valley: Realistic puppets in general invoke this, but this movie may escalate it into Nightmare Fuel. The Gelfings are particularly just-human-enough to be eerie, as are the creepily baby-like Podlings. Many of the other creatures are similar enough to real animals, anthropomorphic or otherwise (vultures, crabs, etc.) All together, they are prone to give the viewer a slight case of the willies, at the very least.
The Gelflings are closer to human in appearance than any of the other puppets — and perhaps for that very reason, some viewers tend to find them the least convincing.
The gelfling muppets have no capability for facial expressions, which is darn odd for the main character when considering the amount of effort put into the others.
What Do You Mean, It's Not for Kids?: That is, not for young kids (age 3-5). Despite Jim Henson being the director, this movie is no Sesame Street (or Muppet Show for that matter). The story is pretty dark for a Jim Henson production and there are some scenes in it that can be considered unsuitable for young viewers, like when the Skesis drain the Podlings (and Kira) of their vital essence.
Woobie: YMMV, but for the first hour of the movie the chamberlain isn't shown doing anything evil, except for that whimper of his. And twice tries to talk peace with the heroes. It's hard not to feel a little for even a bad guy when he says he comes in peace and in return the hero stabs him. Also he was stripped of his rank and clothing, so it was easier to pity him.
The Mystics, being the good halves of the Urkskek that make up them and the Skeksis, have seen several of their fellows die suddenly without much reason and likely knowing what the Skeksis are planning, but are too peaceful (and apathetic) to do anything.
The Skeksis. Unlike the uRu, they were absolutely delighted with the separation from the Urskeks, and have no desire to merge with their other halves. They're self-serving, hedonistic, outright murderous creatures, but they're also locked in a desperate struggle to simply carry on existing.
Aughra is very much the spiritual guardian of Thra. She is forced to watch her world be ravaged, polluted and violated for a thousand years.
In fact, every single character is a woobie to some degree.