All There in the Manual: The novelization by J.M. Dillard does a lot to redeem the movie's Idiot Plot, adding considerable backstory to Sybok and his mother, and explaining that "God" had telepathically sent Sybok a formula for configuring a starship's deflector shields to penetrate the Barrier. After Sybok orders Scotty to set up the Enterprise's shields in this way, Klaa's Bird-of-Prey copies the same shield configuration in order to follow the Enterprise.
The Alleged Ship: The Lemonprise. Kirk is nonplussed by his squeaky chair, dodgy transporters, and the defective Log transcriber (which keeps popping open with ridiculous SPRONNG! noises).
Artists Are Not Architects: In one scene, the Enterprise is shown to have about twice as many decks as it could possibly contain, and they are numbered in reverse order for some reason.
Somewhat explained in the Alternate UniverseStar Trek: Myriad Universes story "The Chimes at Midnight"; Kirk was at one point forced to climb the turbolift-shafts and to count the decks as he passed them, "for they were not labeled on the interior of the shaft, although he noted with annoyance that the designers had elected to number the numerous individual turbolift landing decks—each level having several turbolift stops along its breadth—as he passed a sign misleadingly indicating 'Deck 52.'"
Ass in Ambassador: Inverted, unusually for Star Trek. St. John Talbot and Korrd are not unreasonable people (just incredibly jaded), and Caithlin Dar is downright nice (a rarity for Romulans, actually...).
This may be precisely why they are where they are (particularly Korrd, who is both disgraced and disgraceful in his drink): The planet is a dumping ground for anyone in the diplomatic corps of the three powers that the leadership wants to be rid of in a non-permanent way. If they hadn't gotten along, they would have died.
Behind the Black: Scotty, after claiming to know the ship like the back of his hand, concusses himself on a bit of bulkhead that sticks out from the wall. Whilst unseen by the audience before impact, Scotty was walking towards the bulkhead and, in fact, was looking right at it when he hit it.
Big Bad Ensemble: Sybok and Klaa are an unusual example in that Sybok isn't really evil per se, and for the most part Klaa is more of an annoyance than anything else.
Big Damn Gunship: Spock, commanding a Klingon Bird of Prey, opens fire on "God" in order to rescue Kirk.
Big Ego, Hidden Depths: Sybok. Cruelly invoked by "God", who takes the form of Sybok and mocks, "What's the matter? Don't you like this face? I have so many, but this one suits you best."
Call Back: Kirk states in the opening that men like himself, Bones and Spock had no families. He later admits he was wrong.
Cannot Tell a Lie: What Spock claims as proof that Kirk was not aboard the Enterprise. He was lying about not being able to lie, though he was telling the truth about where Kirk was at.
Canon Discontinuity: It's still technically part of the canon, but the events have never been directly referenced in another canonical Star Trek work again. Rumor has it the writers are specifically told not to as a matter of course. Gene Roddenberrysaid he considered some elements of the movie apocryphal, but he apparently never told anyone which ones. Ronald D. Moore, who was working on Star Trek: The Next Generation at the time, has said that while the writers of the show accepted the film as canon, they considered it such an embarrassment to the franchise as a whole that they agreed among themselves that they would never reference it on the show, to the extent where the ending of the episode "The Nth Degree" was heavily rewritten simply because they didn't want it to have have anything in common with this film.
The novels, which are now vetted more thoroughly than they used to be, have featured Sybok exactly twice, both of them in the Myriad Universe novels, which take place entirely in alternate universes.
The novels have also mentioned the God-like creature at the center of the Great Barrier; in the Q Continuum trilogy of novels, He referred to Himself as "The One", and was a contemporary of 0, the Beta XIII-A entity, and Gorgon. The four of them were responsible for the destruction of the Tkon Empire. It is mentioned that pretending to be God and then using the resulting influence to drive civilizations to self-destruction is his entire schtick. In fact, he was imprisoned in the center of the galaxy by the Q for his crimes, while 0 was punished by being thrown out of the galaxy (which was the reason for the galactic barrier as seen in the 2nd TOS pilot).
The only real survivor, at least according to the Okudas in the Star Trek Encyclopedia, is Captain Klaa. Who was apparently bumped down for his actions and assigned as a courtroom translator in Star Trek VI. This was due to a coincidence in that the translator was played by Todd Bryant.
Cerebus Syndrome: The "comedy" disappears and the movie becomes much more serious once they begin their trip to the Great Barrier.
Chuck Cunningham Syndrome: Both inverted and possibly played straight. While the obvious inversion is Sybok, who is revealed to be Spock's half-brother, we later have Kirk note he had a brother once, who he lost and was lucky enough to come back, referring to Spock's resurrection. However, the way Kirk says this sounds like he's forgotten he actually did have a brother who was lost, (George Kirk Jr), who was killed back in the classic series.
Crapsack World: The Planet of Galactic Peace. As is pointed out by many reviewers (including SFDebris), Nimbus III neatly scuttles Roddenbery's tenets regarding the future: the planet set aside for the mutual cooperation of three races has fallen into anarchy, the technology of the future has turned to rusted crap, and poverty is still rampant.
Ironically, one could argue that it succeeded in establishing galactic peace... as the various ambassadors are either too drunk to bother fighting each other or have grown united in their shared hatred for their own governments for assigning them there!
Cultural Rebel: Sybok, who is definitely the most emotional Vulcan we've ever seen.
Custom Uniform: Each of the Power Trio is given an alternative uniform, which looks not unlike a grey pullover/sweatshirt. Captain Kirk is also seen in a "Captain's Jacket" at one point, underneath which he wears a white t-shirt bearing the slogan "Go Climb A Rock".
Darker and Edgier: Shatner wanted to depict an edgier future, so we got a desolate city named "Paradise", a barely functioning Enterprise, and the Star Trek Universe's first (but not the last, alas) fart joke. Wow.
Shatner was also (reportedly) never thrilled with Roddenberry's idea of a perfect future, so he had those elements to show a more "realistic" future.
Death from Above: Kirk calls down some Close Air Support from the Enterprise in order to try and cover his escape from "God". While a photon torpedo should have been quite a bit more powerful than shown, it was still cool.
Distracted by the Sexy(?): Uhura does her infamous nude fan dance to distract some mooks so that the Starfleet team can capture them and steal their alien horses; however, see Fan Disservice on the YMMV page. (It was in the dark, and they spotted her from a distance, so it might have made sense in context.)
Don't Call Me Captain: During the camping trip, Kirk asks Spock to call him Jim, reminding him that they're off duty.
Eldritch Abomination: It's never explicitly stated just what exactly the "God" is, but it's clearly an example of this trope.
Everyone Knows Morse: Justified, as Starfleet is one part military, and Morse Code could be part of their training.
Executive Meddling: Paramount forced Shatner to up the film's comedy quotient due to the previous film's success in that area. This results in severe Mood Whiplash between a grand, epic story about the search for god and slapstick farce.
Fake Static: Done twice, once for laughs when Chekov pretends that there is a blizzard to avoid admitting he's lost, and once for drama when the Enterprise broadcasts static to delay talking to Sybok.
False Innocence Trick: The Enterprise passes through the barrier around the heart of the galaxy and finds the legendary planet Sha Ka Ree, believed to be the home of God. When the protagonists find God he's apparently imprisoned there, and tries to trick them into helping him escape. A subversion, because Kirk figures out there's something funny going on and manages to get "God" to reveal his true evil nature before he gets away.
Getting Crap Past the Radar: Literally, and proving that the Enterprise DOES have toilets. Just before Scotty's jailbreak, look at the stencil on the "chair" Kirk is sitting on. "WARNING: DO NOT USE WHILE IN SPACEDOCK".
Heroic Sacrifice: Sybok, when he tries to mind meld with "God" so the others can escape.
Hollywood Tone-Deaf: Of the three schlubs failing to sing "Row, Row, Row Your Boat" in sync, Kelley's singing got him into acting, Nimoy recorded a few albums, and... oh. Well, okay, one of them has an excuse. At least Spock is in tune.
Mercy Kill: Bones relives one of his most painful moments, where his father is dying and suffering from an incurable disease. He begs Bones to stop treatment so that he can finally die. Bones does so, and mere months later a cure for his father's disease was discovered.
Mood Whiplash: Executive Meddling insisted that the film include more comedy after that worked so well in the previous film. Unfortunately, the story here is rather less appropriate for it, resulting in the mood careening wildly between Big Important Events and broad slapstick.
Mythology Gag: The shuttle's name Galileo as well the script it is written by on the ship.
Nobody Poops: Averted, at very least whenever the Enterprise is not in spacedock.
No One Gets Left Behind: Kirk orders McCoy and Spock to beam out first when the transporter conveniently can only beam up two at a time. McCoy calls BS on this mid-beam.
The Only One: A twofer. As well as Kirk being supposedly the best person to send in for hostage negotiations, the Enterprise is apparently the only ship available to take him to Paradise. That's despite Kirk starting on Earth, home of one of Star Fleet's largest bases, and Enterprise's construction not actually being finished.
The Nose Knows: In the turbolift as Kirk and crew return from their camping trip.
Not So Different: For all his talk of rejecting the Vulcan way, Sybok essentially brainwashes people into suppressing their traumatic memories, denying them the chance to deal with their pain. Overall, how this any different than Vulcans suppressing their emotions?!
Not the Fall That Kills You: Kirk falls several thousand feet down El Capitan only to be caught by Spock about a foot away from the ground. Cue to Kirk humorously trying to shield himself with his hands against the rocks that are mere inches below him.
Plot-Induced Stupidity: Sending a barely functioning, untested ship into a hostage situation when it doesn't even have functioning transporters. A hand wave was attempted by saying there were other ships around, but only Kirk had the experience. By that logic, they could have just sent a working ship to meet Kirk. Even Kirk thinks the reasoning is bullshit. Then again, it's just a hostage negotiation.
Also, Sybok's plan to get a starship is overly complicated than just using his pain power to work his way up the Federation chain-of-command to get an admiral to simply lend him a ship and crew.
Explainable in light of the apparently small stakes: three hostages, only one a Federation citizen, an apparently insignificant one exiled to a job he hates on a "worthless lump of rock." It's a job for a ship with nothing important to do. Enterprise is the most expendable ship at the moment, and Admiral Bill's comments to Kirk are obvious flattery.
The Pollyanna: You just get that vibe from Caithlin Dar. She's young, sweet natured, and extremely naive. She contrasts her Human and Klingon counterparts, who are older, more cynical and really stopped giving a damn.
Renegade Klingon: Captain Klaa. He decides to go Nimbus III not to save the hostages, but to fight the rescue ship the Federation is sending. When he learns it's Kirk being sent, it only makes him more eager to attack. It's only when General Koord steps in that Klaa appoligizes for his unauthorized aggression.
Not necessarily an example of the trope. Ships were a lot faster in the original series and other movies set in the same time frame than they were in later material. They could travel to the edge of the galaxy and back in a very small amount of time or map every gas anomaly in the Beta Quadrant in a few months. In the animated series they even visited the center of the galaxy and met Satan.
Also, the Pioneer probe blown up by the Klingons had been traveling at only a tiny fraction of lightspeed from Earth for 300 years, meaning the Klingons would have to be pretty deep within Federation space to encounter it. Of course, these Klingons were explicitly looking for a fight, so it's not unreasonable that they were deep in Federation space.
Screwed by the Studio: Retroactively. While all the other TOS-era films were given "Directors Cut" reedits and re-releases, any of which allowed the directors to make improvements, William Shatner was famously denied the opportunity to put right this film with a Director's Cut, even though of all six original films, it was the one that needed fixing the most.
Scotty Time: Inverted. When Kirk beams up to an Enterprise falling apart, Scotty says "You may have given me too much time, Captain."
Sliding Scale of Idealism Versus Cynicism: As some pointed out, "Star Trek as a franchise had, up to this point, been entirely devoted to an optimistic future of interplanetary peace, technological advancement, and human brotherhood. Star Trek V, on the other hand, is a deeply cynical movie," with the Crapsack World on which it begins, the unreliable technology and the phony God that emerges at the ending as examples of this.
Villainous Breakdown: After having been blasted with a photon torpedo, "God" come out of it as this rather goofy distorted face exclaiming "YOOOOOUUUUU!" while floating after Kirk. This is because the ending had to be radically changed, and they couldn't afford to get the actor back to record any new material.
Well-Intentioned Extremist: Probably the saddest thing about Sybok is that he's sincere. He honestly wants to help people, he honestly wants to do good, and he actually stands up to what he believes is God to demand to know why his "friends" are being hurt.
As extremists go, he is quite moderate. While he does take hostages and hijack a spaceship, he doesn't actually kill or even really hurt anyone (trying very hard to avoid just that), and actually improves the lives of nearly everyone he meets. And while he is endangering lives, he isn't aware of that, and tries to minimize damage where he can.