Americans Hate Tingle: A number of American Gundam fans (the UC fans in particular) really, really loathe this series, declaring SEED Destiny to be the worst Gundam series ever made. Why? Because of this one particular character's Hostile Show Takeover (you know who he is.)
Kira was a Base Breaker in the original SEED, but by Destiny the west had given up on him and he's lost almost all his defenders.
Like SEED, Lacus is unpopular in the west even though she's one of the most popular characters in Japan.
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.
The HD revision 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 rerelease.
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 Breaker: Almost every character in the series gets this. This is how controversial the series is. Some highlights:
Broken Base: Another an AU Gundam series. Probably the most controversial 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.
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.
Die for Our Ship: It's hard to know which girl of the Athrun Harem takes more bashing from fans of the other girls, though Meer and Meyrin get it particularly hard. Not even Cagalli was safe.
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. Athrun/Cagalli are by far the most loved pairing when it comes to sheer number of fanfic written about them. As for Dearka & Miriallia, the first thing she said upon rejoining the Archangel was that she dumped him. 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.
Gladys' son being mentioned only at the end makes sense when you take into consideration she only left Durandal for some unnamed guy because she wanted to conceive. As such it's possible that as she regrets leaving Durandal she has conflicted feelings about her son.
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.
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 statments 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.
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.
Jerkass Woobie: Shinn's an unpleasant little jerk a lot of the time, but that doesn't make what he went through any less horrific. You want to hug him and slap him at the same time. Auel and Sting seem to count for some fans.
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; parts of the fandom hold that his real MEH is when he puts Stella in the Destroy.
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.
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.
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.
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.
Also not helping them is Morosawa's fondness of the Kira/Lacus pairing and how Cagalli was handled.
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.
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.
Subverted with the manga that explains all about the Destiny Plan.
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.
Alternate Character Interpretation: Yuna was always a coward, who was very skilled at manipulating a distraught eighteen year-old girl who was dependent on he and his uncle for political support, but failed the minute things didn't go his way.
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 .
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.