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.
Broken Base: In regards to the 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. Others see it as completely derailing his Character Development, because this ending is unfair after all the hard work he did, and it makes him seem like a permanent outsider.
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.
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.
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.
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 ED, Splash Free, is just as catchy, if not even more so, than the original PV.
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 G/Kou.
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.
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.
Nightmare Fuel: The ending of Episode 5 can be unsettling for beginners who swam in the ocean once.
Rin's violent rage after being taken off the relay and losing his race. Even Nitori is scared by him.
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.
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.
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.
Where Everybody Knows Your Flame: In the ED, the guys are dancing in a suspicious club with shirtless guys wearing masks in the background. O Ps and E Ds are generally pretty weird compared to the actual show, so who knows what's going on.