Like SEED, Lacus is unpopular in the west even though she's one of the most popular characters in Japan.
The reaction in Japan wasn't quite as strong, but even so, the show seems to have as many vocal detractors as fans in Japan. For reference. A lot of this can be attributed to Shinn's demotion, since characters of his type tend to be better received in Japan than in the West.
Author's Saving Throw: The director's cut OVA is favored over the television series' finale for its new animation, the exploration of Durandal's character and the extended ending that expanded on the original that left viewers a really bad taste.
The four-part compilation movie 'Mobile Suit Gundam SEED Destiny: Special Edition' retelling the entire series from Athrun's perspective with some Revision. See the list of changes at The Other Wiki.
While not all of the changes could be retained for the HD Remaster, the latter does it's best to include as much of the material from the Special Editions as it can. This is mostly evident with music introduced in the Special Editions, but also about 90 percent of all of the animation from the Special Editions are used instead of the original broadcast, such as Kira and Shinn's first encounter.
The HD Remaster also got this when the Kira's fight scene in the Strike Rouge was completely remade to take advantage of the mobile suit's capabilities. As a common complaint regarding Kira is that he just "relies on Beam Spam to win", it further shows that, when he's in a weaker mobile suit, he is not completely invincible (the Strike Rouge is trashed in the fight, though he survives), and he can still fight in cool and surprising ways. It is considered the highlight of the HD Remaster.
Awesome Music: The debatable quality of the series does not extend to Toshihiko Sahashi's soundtrack, which is some of the best composed for anime with a seamless combination of orchestral, electronic, rock, and cloral numbers. The theme songs are no slouches either (with the arguable exception of the 4th opening). Whenever you hear T.M Revolution singing you know that Kira (or Shinn in Special Edition) is going to do something amazing.
The 4th opening's actually remarkably good, it's just not a song for an opening. The real problem with the 4th opening (not to say it worked as an opening), was that the new ending theme and previous opening themes were still much stronger than it was, so Wings of Words never stood a chance. When the show was first airing, it was derided (at least among the English-speaking fandom) for sounding like it fit more in a romantic drama than in a mecha war series. It seems the Japanese producers agreed, as the HD Remaster replaces "Wings of Words" with "Vestige" by TM Revolution for the fourth opening.
Base-Breaking Character: Almost every character in the series gets this. This is how controversial the series is. Some highlights:
Broken Base: Possibly one of the most controversial Gundam series ever.
Ask in a forum who is the series' main character and you prepare for one of the longest discussions ever. People will keep repeating the names of Shinn, Athrun and Kira and rarely reach an agreement. It doesn't help that Athrun also happens to be the main narrator from the compilation movies and the one with the most screentime.
Athrun/Cagalli's relationship is a huge source of debate, due to the fact that no one seems to know what is going on with the two by the end. Were they really subjected to Ship Sinking or are they still together, just focusing on rebuilding Orb? The fact that fake interviews and rumors have muddied the water doesn't help this at all. That they are also always depicted together like the other two main couples in the series has also made it even more difficult to tell.
Complete Monster: LordDjibril is Azrael's successor, with all of his predecessor's Fantastic Racism and contemptibility, but none of his intelligence or charisma. Having returned Blue Cosmos to its terrorist roots, he has his minions perform horrible experiments on children, whom he then brainwashed into Child Soldiers; opens the war with a nuclear assault on the colonies; unleashes the Destroy on Eurasia—leading to the deaths of thousands, if not millions, of civilians and the burning of Berlin—personally kills over a million innocents with a Wave Motion Gun while bragging about having the guts to do something like this; and is responsible for turning Mu La Flaga into Neo Roanoke. He exploits the tragedy of the Junius 7 Colony Drop to start another war; forms a new anti-Coordinator alliance; keeps up Azrael's horrible treatment of the Extended, using Psycho Serum addiction-with fatal withdrawal symptoms—and mental rewrites to maintain their loyalty; and continues the practice of raising kids to be the indoctrinated soldiers mentioned in Stargazer. Convinced that his own survival is paramount above all else, Djibril regularly abandons his allies when the going gets tough, and entertains plans of ruling the world when the war is over. Essentially what happens when you give someone with the personality of a low-functioning sociopath and jumped-up school bully access to unlimited resources and technology, Djibril reacts to every problem with greater and greater amounts of brute force and indiscriminate murder, as he tries to simultaneously hang onto his position of power and bring down the curtain on the Coordinators as a race. He's a combination of impotent rage and cowardice, but with the money, influence, and total immorality to make him horrifying instead of merely pathetic.
Critic-Proof: Mobile Suit Gundam SEED Destiny is very popular among the Japanese audiences and even won the Anime Grand Prix award for Most Popular Anime in 2004 and 2005. Western reviewers liked the series but not as much as its prequel. However, if you ever ask this to a Gundam fan prepare to hear how this series is one of the worst things Sunrise ever created
In a nationwide poll conducting what readers of Gundam Ace thought was the best Gundam series Gundam SEED Destiny ranked 12th out of 20 entries despite selling more than most entries that was ranked above it. It's Gunpla sales were also a huge disappointment for Bandai. While Destiny was popular with general audiences most everyone were highly critical of it.
Fan-Preferred Couple: This show sankboth Dearka/Miriallia and Athrun/Cagalli. Considering that both of those pairings were quite popular among the fandom during the first show's run, the reaction was predictable. The fandom's solution is to have them make up after the series ending and get back together again, if fanfic is any indication.
Although she was present in Gundam SEED, the fact that Shiho appeared more frequently in this show upped her popularity and really kick-started the Yzak/Shiho fanbase. Prior to this, fans of Yzak looking to pair him with someone tended to do so with either Dearka, Fllay (simply due to the fact that she was the only major female character he was around late in the series), or even Cagalli. Once people started noticing Shiho, she quickly became the favorite for Yzak, and the other pairings were largely forgotten.
One major reason for Destiny's problems is the What An Idiot tendencies of the cast. Except...not really. First, compared to SEED which didn't reveal the Big Bad until later on, Destiny early on reveals who the Big Bad is. Second, no one in the cast knows this or has enough proof to do anything about it. Alternatively, they aren't in the right place to do something about anything or already are being manipulated quite thoroughly by said Big Bad. Third, aside from the majority of the cast being teenagers, the returning cast also has a lot of PTSD to deal with from the previous war. The idiot tendencies make more sense with a) some of the idiot stuff only seems that way to the audience who knows more and b) no one is very mentally sound due to the previous war and other contributing factors.
"Funny Aneurysm" Moment: All of those rants about Chiaki Morosawa ruining the show, along with those hoping for her death from her illness as "punishment" for "ruining" the series", were already seen as insensitive and mean-spirited before she actually died in February 2016. And after she kicked it...
Some people mocked Shinn being tied to his sister's phone, more specifically, listening to her voice on the answering machine. Criminal Minds had a situation where a man lost his girlfriend and unborn child in a deadly gang attack. Less than six months later, he gone on a brutal killing spree n revenge. One element of his character, listening to his girlfriend's answering machine. Not exactly funny.
Germans Love David Hasselhoff: Despite being hopelessly irrelevant, the Blast Impulse is very popular with western fans for its unique color scheme and payload. It's almost completely ignored by Bandai, not even getting a regular 1/144 High Grade release or a Master Grade release at all.
In episode 23, the insert "Meteor" by TM Revolution plays before the death of a character voiced by TM. The fact that the theme ended just before the character was killed made people wonder if decided to sing before being killed.
Gilbert and his speech about his Destiny plan is humorous when you realize Wufei made statements about "getting rid of all evil" (both characters are voiced by Ted Cole). And in the Endless Waltz, Wufei was even willing to become evil to achieve peace.
Sting's "I'm practically non-existent to you, am I?" quote (coincidentally) foreshadows a long-running meta joke (the men's existence) in the Love Live! franchise.
Internet Backdraft: The amount of flame wars started by the mere mention of this series, as well as Kira and Lacus' names in fan forums is staggering.
Shinn's an unpleasant little jerk a lot of the time, but that doesn't make what he went through any less horrific. Many viewers want to hug him and slap him at the same time, screaming at him "YOU IDIOT! STOP RUINING YOUR LIFE AND OTHERS'!".
Auel and Sting seem to count for some fans, as they're massve jerks but are also mere pawns in this "game" of war and, as members of the Extended group, are deeply fucked up in all senses.
Moral Event Horizon: Djibril and the EA cross it for good when they unleash the Destroy on Eurasia. Durandal crosses it when he uses Requiem to force the rest of the world to fall in line with his plans. In-universe, Neo Roanoke reflects that he crossed his personal MEH when he started brainwashing children for Djibril.
During one of her first sorties with the Impulse, Luna has an opportunity to destroy a shuttle carrying a fleeing Djibril into space. She misses and he escapes. This one thing has eternally defined her character for some people, though it was already established in episode 7 that Luna was a lousy shot during her target practice sessions. (Which makes it more Talia's fault for assigning the long range bombardment weapons to the worst shot of the trio.)
Gundam Seed Destiny itself is considered a huge case of Never Live It Down. After seven long years since the end of the series, and even after its more popular handling in the Super Robot Wars games, haters will never get over their hate towards the series and its characters.
Athrun's role got some criticism to the point of being listed as the dumbest Gundam character in an official Sunrise poll.
People often like bringing up Shinn whining about his parents and sister when in the show he stopped doing it openly pretty quickly.
Djibril's vaporization, one of the most graphic of such deaths in the franchise.
The episode where the Minerva crew finds the facility that made the Extended pilots like Sting, Stella, and Auel, complete with video recordings of the process used to make them, which actually causes Arthur to vomit.
Replacement Scrappy: Shinn, who seems to have been an attempt at creating a darker, more conflicted Kira. It didn't work. It should be noted that Shinn was the third most popular male character in the CE franchise (behind Kira and Athrun), based on the then-current NewType and Gundam Ace character polls.
Ron the Death Eater: Fans who disagree with Kira and Lacus' tactics often forget their motives and try to turn Kira into Rau 2.0. The actual Rau 2.0, Rey, also suffers from this at the hands of fans who Flanderise him into an irredeemable bastard, while forgetting his admiration for Durandal, good intentions, and what may have been a genuine friendship with Shinn. Which ironically demonstrates the flaws in the Destiny Plan that Rey believed in so much; he was genetically identical to Rau yet a distinctly different person.
Rooting for the Empire: The numbers of those who were already rooting for the Earth Alliance in the previous series (since it had some sympathetic POV shots) swelled when they practically became Card Carrying Villains in this one. It did not help that some of the portrayals came off as political Take Thats. The people who root for ZAFT, conversely, tend to fall under Draco in Leather Pants.
Scapegoat Creator: The level of hatred that the most rabid anti-fans deliver towards Fukuda and Morosawa sometimes reaches disturbing levels. It doesn't help that they have a reputation as Lying Creators that may be entirely due to poor fan translations of the relevant interviews, plus a supposed "Morosawa interview" that was apparently fully made up by haters.
The Scrappy: The Broken Base may fight over just about every aspect of Destiny, but just about nobody on either side likes the DOM Trooper pilots. Poor characterization plus overuse of Zeon Expies equals Black Tri-Stars clones who spout lines like "You'd have to be pretty messed up to disagree with Lacus-sama!" Shinn fans hate them for being one-dimensional zealots, while Kira fans hate them for Not Helping Their Case. Even many Kira fans were left wishing that that Shinn or Luna would subject the DOM pilots to the Black Tri-Stars treatment, especially since that would've made the finale seem like less of an unrealistic Curb-Stomp Battle and more like something Kira's side had to actually work for.
Strangled by the Red String: Shinn's and Lunamaria's respective first loves are Stella and Athrun. Stella dies tragically, Athrun, along with Lunamaria's sister, Meyrin, defect, are shot down by Shinn and presumed to be dead. They got better. Lunamaria and Shinn end up together but due to the way it was handled, they are widely believed to have been this. The Special Edition is a little better about this.
Tear Jerker: Meer's death by Taking the Bullet for her idol-turned-enemy Lacus Clyne. Not only is it a massive Tear Jerker, it's also one of the few instances in the Cosmic Era where we see Lacus actually angry.
A lesser one is when Cagalli is told what the pilots said about Patrick Zala being right, considering that she had been there with Athrun when he had died, and had even helped hold him. She knows more than anyone else just how poisonous Patrick Zala's hatred was, as well as how it affected Athrun and she can't do a damn thing to help him.
They Wasted a Perfectly Good Plot: Basically nothing about Neo Roanoke's identity is played to its full potential; most of the implications (such as the parallels between his situation and the Destiny Plan) are never even addressed, let alone things the fanbase was made to expect, like an armed conflict between Phantom Pain and the Archangel. Nor did they bother to have him become The Atoner for the horrible things he did while brainwashed, instead just having him go straight back to being SEED-era Mu La Flaga as if regaining his old memories caused him to forget all about being Neo.
Subverted with the manga that explains all about the Destiny Plan.
The halfway mark of the series has the Minerva crew discover the lab where the Extended were created, and see the records of exactly what horrible things Lord Djibril did to make them. It's treated like a big important moment in the story...that never comes up again.
Tough Act to Follow: Even though it was still a ratings success, it was preceded by the show that had the second highest ratings in the franchise. There was no way it was going to keep up that momentum, which resulted in the perspective flip as well, to try and up the ratings.
Vindicated by History: Many will outright praise its handling in Super Robot Wars Z which means that Destiny had lots of good ideas and concepts, it was just how they were executed that pissed a lot of Gundam fans off .
While the series itself is still controversial, it has mostly been given a re-evaluation thanks to both Super Robot Wars and the introduction of Mobile Suit Gundam AGE, the latter of which is widely regarded as far worse.
What An Idiot: While most instances can be easily disputed, Athrun has a severe case of Aesop Amnesia that causes him to make poor decisions in situations where fans think he should have known better. However, Athrun's Patriotic Fervor and PTSD may have also been a factor in the amnesia's onset. It's kind of justified from the writer's perspective (a major theme in Destiny was how people can commit the same mistake repeatedly), but whether it's handled well is a subject of furious debate.