Americans Hate Tingle: Flay is a Base-Breaking Character in the west. Not so much in Japan, where she's generally well-liked. Which is ironic since the director had actually thought she'd be the type of character to appeal to Western audiences, but things ended up reversed.
Flay is a polarizing character. She spends much of the first half of the show being manipulative for a sympathetic-but-unjustified reason, and later attempts to make up for it. Either she was a Jerkass Woobie who redeemed herself in the end, or a selfish asshole too wrapped up in her own problems to empathize with anyone else and her later actions were too little too late.
Lacus, given her status as an idol singer, which some fans feel doesn't fit really well with the series' tone. Her turning out to have a large political clout while being a teenage idol singer also pushes Suspension of Disbelief a little thin even though such role is preferred over an idol. Her worst critics argue that she comes off as a hopelessly naive person who lucks her way into victory and power. However, there are plenty of people who feel that her portrayal as a Relena Peacecraft-esque alternative political figure works fine, and even some who don't mind the Idol Singer angle.
Kira himself. For everyone who hates the "Jesus Yamato" angle and finds it makes him overbearing and boring, there's someone who finds him awesome and likes that at least one Gundam protagonist is willing to actually stop killing people instead of doing it and then endlessly Wangsting about it.
Broken Base: In the HD Remaster, Nicol's death was retconned to make it appear largely accidental. In the original, he attacks, Kira counters, and the attacker is killed. In the remake, he attacks, Kira dodges, and the attack carries him into Kira's sword, which kills him. Here's a comparison video. The base is split over whether this is an example of The Dog Shot First and an attempt to make Kira less responsible for his death, or whether it's a minor choreography change that doesn't really mean anything.
Muruta Azrael. Some fangirls either downplay or handwave his atrocities in the show because he's so pretty and hot.
Shani, Clotho, and Orga get the same treatment. Yes they're Slave Mooks forced into the war by Azrael, but that doesn't make them any less vicious or insane.
Do we even need to bring up Rau Le Creuset and the leather pants fangirls give him?
In the case of Rau and Azrael, people that hate the show also love them because they desired genocide and said haters are of the opinion that Cosmic Era is a horrible world that deserves for everyone in it to die.
Despite his Sacrificial Lamb status and being The Faceless, Rusty Mackenzie is surprisingly popular among the fanbase.Supplementary materials have helped a lot, revealing him to be a friendly guy who was the only Redshirt of the Le Creuset team who didn't have a parent on the PLANT ruling council.
It's the Same, Now It Sucks: This series is the AU series that is the most like the UC shows, due to the similarities between the Earth Alliance/ZAFT and Federation/Zeon conflicts, which might be a factor into why it's a frequent target from UC fans.
He's also clever enough to maintain his facade of wholesomeness until well after (in his mind at least) his plans have reached the stage where no logical reason remains to believe they can be thwarted. Rau Le Creuset isn't going mad during the final battle; he's having the time of his life. He even dies with the absolute belief that he is taking the whole of mankind with him - as evidenced by the almost seraphic smile on his face just before GENESIS obliterates the Providence.
Mis-blamed: As mentioned many times on this page, many of SEED's detractors take Destiny's flaws and put them onto SEED instead of focusing on SEED's own flaws. In fact, even though there were a lot of changes in production just like Destiny, they improved the overall quality of the series. Not that the Fan Dumb will listen when you bring this up, of course.
It's easy to lose respect for Rau Le Creuset when he nonchalantly uses his DRAGOONs to kill Flay Alster, who had by this point redeemed herself.
And then there's Patrick Zala shooting Athrun. And pretty much everything Azrael does, most notably using Psycho Serum to turn kids into Super Soldiers, and using nuclear weapons as though they were going out of style. Captain Sutherland and the Earth Forces as a whole crossed it after the incident at JOSH-A with the Cyclops system.
Depending on who you ask, some members of the fanbase feel that Yzak Joule crossed this when he shot down that shuttle. Even taking what he thought was going on into account, he still believed he was firing on fleeing soldiers, a less than admirable act. This is possibly the reason why in Super Robot Wars Alpha 3, that scene was modified and the civilian shuttle was shot down by random ZAFT pilots, rather than Yzak.
Never Live It Down: If fandom is to be believed, then Kira's a bad pilot and Flay's an irredeemable bitch.
One-Scene Wonder: The Perfect Strike in the HD Remaster. Only appears in two episodes (the Battle for Orb) and is never seen again (despite being edited into the 5th opening).
Rooting for the Empire: Some fans ended up rooting for the Earth Alliance because of the insane disparity between the kill ratios between the Alliance and ZAFT. Especially since many sympathetic POV shots indicate that most of those poor Earth Alliance bastards getting killed are just doing their jobs at the behest of raging bigoted lunatics instead of being raging bigoted lunatics themselves.
The fact that the EA soldiers and pilots are also all normal people while ZAFT is entirely made up by what the show directly states to be genetic engineered super humans further enhances this feeling. It also doesn't help that the first high-ranking Earth Alliance official we really get to know, Admiral Halberton, was a pretty cool guy who shot down Natarle's suggestion that they conscript Kira into the military. He ended up dying tragically with his command, the 8th Fleet which was completely wiped out except for the Archangel.
They Changed It, Now It Sucks: The Remastered version is by and large the same, but there are small touch-ups and additions of scenes here and there. One notable instance is in episode 36 which adds a shot of Shinn and his family trying to flee the fighting. Probably the bigger change is in the ending themes: the first ending theme was remade and sounds somewhat different, while the original 2nd ending theme "River" by Tatsuya Ishii is omitted entirely and replaced with a new song by FictionJunction. Predictably, some fans of the original run have reacted much in the same vein as "Han shot first."
They Wasted a Perfectly Good Plot: Sort of. English-speaking fans often mistake a brief conversation between Siegel Clyne and Patrick Zala as this. In one scene, the two discuss the fact that few Coordinator children are being born in the PLANTs, and it's mentioned that some people have been advocating for Arranged Marriages in order to encourage people to start families (including Clyne and Zala themselves — this is exactly why Athrun and Lacus are engaged). This is a reference to the real-life social issue in Japan of an unsustainably low birth rate (literally; their population is getting smaller because more people are dying than are being born), but many English-speaking fans understandably miss the reference and believe it's an indication that Coordinators are becoming infertile due to their genetic manipulation, and are confused when the issue is never raised again.
Viewer Gender Confusion: Several viewers thought Nicol was a girl based on his looks, voice, and gentle mannerisms.
Iron Woobie: Go ahead life. Torture Kira. He'll get over it, eventually.
Athrun Zala can also be considered this. Lost his mother in a nuclear strike, has to fight his long lost best friend, watches two of his closest friends and allies die due to his hesitation to fight Kira, has a General Ripper for a father, and is too socially arkward to emote or channel any of this grief until it boils over the top and he breaks down. Yet, he still manages to be possibly the best pilot in the series.
If you're charitable to Lacus, she fits in like a hand to a glove. She's sheltered and ultra naive. — but when the chips come down, she does her best to gather her resolve and do what she can to help. Only once she breaks down, and that's when she cries in Kira's arms while telling him about her dad's death.
Jerkass Woobie: Flay Allster, especially once she has her Heel Realization and tries to redeem herself. On one hand she's a self-absorbed, prejudiced and flawed Fille Fatale who's hellbent on revenge and manipulates the hell out of Kira. On the other, she's also a desperate girl who pretty much lost everything and barely knows how to handle herself in the world until her Character Development kicks in.