These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: Either Rin is a completely broken person who needs a big hug, or a selfish monster who should never be allowed near a pool.
To a lesser degree, Nitori; while he has quite a few fans (and is even listed under Ensemble Darkhorse on this page), a decent section of the fandom finds him annoying.
And now Sousuke. Overly protective as a result of a misunderstanding, or a bully who thinks he knows what's best for Rin better than Rin does?
Broken Base: In regards to the Season 1 ending. A lot of people see Rei's decision to give up his spot on the relay for Rin as an incredibly kind gesture and the perfect ending for his Character Development, since it's a sign of how much he has grown and how by putting the teams' needs over his own, he's given them a much bigger chance to win the Nationals. Others see it as completely derailing his Character Development, because this ending would be unfair after all the hard work he did, and it makes him seem like a permanent outsider.
The second season in general has caused a lot of divided opinions. There's a fairly equal split between those who consider Eternal Summer to be either badly written or simply dull compared to the first season and those who consider its differences to be an improvement from the first.
Cargo Ship: Haruka X Water, Makoto X Shovel, Makoto X Water Bottle, Rin X Goggles, Nagisa X Hoodie, etc, etc.
HarukaXWater can be argued as canon after episode six, which has Haruka recount an encounter with a waterfall when dared to tell a story about his love life.
Crack Pairing: Makoto x Shovel was the most popular crack ship prior to Episode 1.
Die for Our Ship: Thankfully defied; when two female characters (Gou and Amakata) entered the fray, the fandom sought hard to defy this trope and determined on waiting before actually attacking them. Sadly, there has been some Het is Eweven BEFORE the twogirls appeared. But in a lighter note, fandom immediately started shooting it down. So it pops up every now and then, but unlike other fandoms where Yaoi-loving fangirls are pretty much expected to hate on every female character in sight, most fans of Free! tend to like the female characters and call other fans out on their immature behaviour.
Regarding Gou, it helps a lot that there's implications in the show that Seijuurou, a minor character who is the captain of Rin's swimming team, has a crush on her, and since he isn't generally paired with anyone else, even hardcore yaoi shippers tend to like Seijuurou/Gou, if only as a side pairing. And since Ama-chan is the boys' teacher, hardly anyone ships her with them anyway. And in the second season, Seijuuro's younger brother Momotarou has also developed a crush on Gou, so...
Most fans are still doing their best to avoid this, but the ship war between Makoto/Haru shippers and Rin/Haru shippers is beginning to heat up. Even more so after episode 7, when Rin defeats Haruka in a swimming race, saying that he will never swim again with Haruka after his less-than-graceful reaction to this, which has the Makoto/Haruka shippers out for Rin's blood.
Sousuke may become the next prospect target, however...
Double Standard: From both sides of the fence; some people who usually enjoy fanservice that appeals to them attack Free! for its fanservice that appeals to others but not them, while people who would attack fanservice in general and shame those who like it would then revel in Free!'s fanservice.
Ear Worm: Pretty much most of the music released thus far, but especially the music from the original commercial.
The first ED, Splash Free, is just as catchy, if not even more so, than the original PV.
The second ED, Future Fish is pretty memorable too.
More-or-less Secondary Character (and captain of the Samezuka swim team) Mikoshiba Seijuuro is also getting quite more popular with each episode, and being the one characters to normally be shipped with Gou.
Aichirou Nitori has gained a following as well.
Nothing trumps Uozumi and Minami—if the names don't ring a bell, they're Samezuka's Those Two Guys in Eternal Summer. You'd be forgiven for not even knowing that they had names, but Tumblr fell in love with them instantly.
Kisumi is also incredibly popular despite only showing up briefly. It doesn't help that his name sounds like "kiss me" (cue fan art).
Fandom Rivalry: Fans of Free and fans of K-On!note or just about any moe/slice of life anime with lots of cute girls doing cute things, but especially K-On! tend to hate each other's guts. Basically, both sides claim that their favored show is the best thing since sliced bread and the other is shallow pandering and/or personifies everything that is currently wrong with the anime industry. Bonus points if neither side realize that both shows are actually pretty much the exact same thing, except genderswapped.
And the Yu-Gi-Oh! ZEXAL fandom, over a misunderstanding where Free! took one of their ship names.
Fanfic Fuel: The ED of Eternal Summer, which shows the cast in different careers, has given rise to multiple alternate universe fanfics - some of them including various pairings the author enjoys.
It's already smirk-worthy when Rin accuses Nitori of being his stalker but when you remember that a year before Mamoru Miyano voiced K's Saruhiko Fushimi, a textbook example of a Stalker with a Crush, this gets an additional snicker and a fond "You hypocrite."
One fanfic written after the end of Season 1 correctly predicted a red-headed energetic newcomer to the Free! cast who was a relative to one of the canon characters. Even the character's motif animal, the sea otter, was predicted! Fun Fact At least, initially. After Momotaro's reveal, his motif animal was since changed to a sea horse. Other than that, the only difference between Momotaro's reveal and the fic is that the relative there was the discarded character Kaede, repurposed as Haru's relative.
Remember when fans speculated during the PV era that Rin would join the swim team to pick up chicks? Momotaro is essentially that prediction come to life.
Makoto and Nagisa also certainly qualify, as well as Rin's new teammate, Nitori Aiichirou.
All of the kids when they were younger.
Narm Charm: This show takes swimming waayy to seriously, but that's kind of the point and the fans love it.
Never Live It Down: From the way it's talked about on the Internet, you could be forgiven for assuming the show is nothing but a plotless collection of scenes where guys take their shirts off.
Periphery Demographic: Despite being an obviously female-oriented series, it has nonetheless its share of straight male fans. As said above, they tend to be drawn to the humor aspects.
Rescued from the Scrappy Heap: Though Sousuke is still somewhat of a Base Breaker, The Reveal at the end of Episode 8 followed by his scenes in Episode 9 and Episode 10 caused a lot of fans who previously disliked Sousuke to change their minds and brought out a lot of sympathy for him.
Selective Squick: The show's vocal male Hatedom is pretty pissed off to see a female-oriented anime getting such a following, especially when the Fanservice is aimed at women and not at men.
Shipping Goggles: Especially prevalent in the original PV, where fans were writing fanfiction based on less than ten seconds of interaction between the boys. Case in point.
Ship-to-Ship Combat: Tensions between Rin/Haruka and Makoto/Haruka shippers had been brewing through Episodes 1-5, but after Episode 6 it seems the sparks of animosity have ignited between the two groups. It got worse in season 2.
Newish he's a returning character from High Speed! character Sousuke inspired this in record time* you could say... with high speed. He's got a childhood connection to Rin, meaning RinHaru shippers feel threatened by the potential existence of new ship SouRin. Some even pre-emptively accused MakoHaru shippers of Pairing The Spares so Rin won't be a threat to MakoHaru. Bear in mind that at the point in time these feelings erupted, this character had only been introduced in the promotional material for season 2. He didn't even have a canon color scheme yet.
Of course, this works both ways. Since Sousuke had only appeared in promotional material, they really had no way of knowing what he would be like in-story. Even so, people (mainly MakoHaru shippers) were eager to pair him off with Rin. The day Sousuke was announced (within the hour, in fact), quite a few MakoHaru fans on Twitter declared that Sousuke would destroy RinHaru and preemptively declared RinHaru as sunk.
It turned out to be nothing compared to Episode 9 of Season 2.
What an Idiot: Yes, Rei, go ahead and swim. You're an inexperienced swimmer practicing at night, in open ocean water, while everyone else is sleeping. What could possibly go wrong?
For some, the mere fact that the team organized a swimming camp near the sea... with a guy who barely can swim among the assistants. It's often remarked in real life that you must never EVER try learning how to swim in open ocean.