Broken Base: Viewers are generally divided on the first 10 or so episodes of the first season. Some hate how confusing they are, as the viewer is locked out of the loop on just what is going on, while others appreciate how much it all makes sense upon a rewatch.
The show's premise, as a whole. Some people see it as just another Evangelion rip-off, while others laud it as one of the best mecha anime of the decade. And then there's the middle group, who like the show but don't think it's anything amazing.
The nature of Kazuki and Soushi's relationship, left ambiguous, has resulted in this. Some people can't see them with anyone else but each other and took the ending of Heaven and Earth as practically cementing their status as an Official Couple. However, they have been dismayed at the lack of focus their relationship has received in Exodus, which hints that Soushi might actually have romantic feelings for Maya, helped by an official relationship chart that states his feelings for her are "romantic?", the question mark leaving it purposefully ambiguous. The fandom is extremely divided on this, either outright rejecting the idea based on the insane amount of Ho Yay and actual Ship Tease between Kazuki and Soushi up to this point or embracing it, stating that it's been there in subtext since the first season and that it's just progressing slowly albeit naturally. Of course there is always the issue of Maya being very much not interested in Soushi in any way other than as another person to protect Kazuki with and that the preferential treatment Maya gets from Soushi in the first season is only done as a favour to Kazuki (see Dramas). This gets lampshaded by Soushi himself so take that as you will.
The focus on the third-generation pilots. Some people think it's a refreshing change of pace, while others would rather the show spend more time with its older and more established characters.
Almost everyone agrees that Exodus ended on a rather hurried state after Episode 19. However, fans are divided that if the Second Season helps to maintain the franchise's good reputation, or pushes Exodus into a Contested Sequel and even Sequelitis.
Ensemble Darkhorse: Canon. She shows up more than halfway through the original season and is one of the most beloved characters on the show. This makes her eventual death even more painful for the fandom.
Mizoguchi is a Badass NormalFriendly Sniper who's managed to survive despite his dangerous line of work. At this point, fans will be very upset if he kicks the bucket.
Fanon Discontinuity: Exodus suffers from this even among fans who genuinely enjoyed the season. This is due in part to the bad treatment of Soushi's character, the dramatic decrease in focus on Kazuki and Soushi as a pair plus Kazuki's seeming indifference to things that would have hit him hard before note For example Soushi jumping in front of a gun wielding Human Army soldier to protect him is never brought up again and, far up on the list, the Downer Ending. "Until The Beyond gives us a happy ending Exodus didn't happen and Heaven and Earth is the REAL ending of the series," basically.
Fan-Preferred Couple: Soushi/Kazuki in large parts, if not the majority, of the fandom. Look on tumblr and you'll find quite a lot of posts calling for them to become the Official Couple; Soushi/Kazuki seems to be popular in the Japanese fandom as well, considering the amount of fanart of the pairing on Pixiv and the results of a "favorite line" pollnote Three out of the five winners are considered to have significant subtext between the two, with #2 being a borderline example, though there's always the possibility of "poll bombing.". While the pairing isn't universally accepted, most fans recognize the subtext. It doesn't help matters that angela love to write songs that play this up even further. Not to mention the Dramas, written by Ubukata himself, that play this up even more and go from a possible Relationship Writing Fumble into blatant Ship Tease.
Harsher in Hindsight: Shouko Hazama suffers from a chronic disease and ultimately dies. Then just a little more than a decade later, her voice actress, Miyu Matsuki, dies from pneumonia.
Hilarious in Hindsight: The existence of an Akane and her son Kazuki becomes this if one is somewhat familiar with anime directors. More specifically with a man named Akane Kazukinote Kazuki Akane for westerners who worked on quite a bunch of? Yes, mecha anime.
"Holy Shit!" Quotient: Episode eight of Exodus Second Season had a very high one, being the probably worst Wham Episode of the franchise, easily outdoing the first season.
...or not given that not only does Maya repeatedly state that she is not the one Kazuki wants, but also that the series develops more and more towards Kazuki and Soushi as a potential item...
Basically, the only thing keeping them from being "official" official is that it hasn't been explicitly stated (Maya's above comment notwithstanding). It's all there on the screen, it's just lacking the words.
Rewatch Bonus: The first 10 episodes are intentionally designed to let the viewer know only as much about what's going on as Kazuki does, which amounts to about jack shit (and is the reason those episodes aren't considered very interesting to watch your first time through). Second time through the series, there are tons of little things that make complete sense now that you understand the nature of the Festum.
Ship-to-Ship Combat: While arguments over ships are generally much more civilized and polite than in other fandoms, there are vehement defenders of both Soushi/Kazuki and Soushi/Maya. The only thing that people can seem to agree on is that Kazuki has some sort of feelings for Soushi, regardless of whether or not they're returned, mostly because the subtext is rampant and because Maya even acknowledges it outright. It's not uncommon however for Soushi/Maya shippers to change their minds in favor of Kazuki/Soushi when pointed towards the Drama CDs which elaborate on many of Soushi's actions throughout the original series.
They Wasted a Perfectly Good Plot: The pain flashbacks Soushi gets through connecting to pilots with the Siegfried System could have been milked for tons more drama. Instead it gets only one mention in both seasons (in Exodus only indirectly in that the pain killers he has to take are habit forming) and one instance of actually seeing it to show that Soushi does care.
Heaven and Earth is bursting with Scenery Porn, from the ocean, to the island, and the sky. Even when Festum takes that sky and turns it dark, its still beautiful and Festum shielding Tatsumiyajima from getting nuked is a truly breathtaking visual. Not to mention the assimilation crystals.
Exodus takes everything good about the movie and turns it Up to Eleven. Scenery, fight scenes, assimilation crystals...it's all top notch.
What Do You Mean, It's Not Symbolic?: Tatsumiya Island uses a lot of Norse mythology for its suit and weapons nomenclature, including the eponymous Fafner, Lindwurm, Fenrir, and Garm, but it's also perfectly willing to borrow from Greek (Medusa, Aegis, Titan), French (Durandal), and Hebrew (Solomon). The UN variants are named for the Greek words Megatherion (Great beast) and Gnosis (revealed knowledge), and the city of Babylon. The Festum cores are named Mir (Russian for peace/world).