In Free!, Rin is shown to have sharp, pointed teeth (like a shark). I would say it was just stylistic, but it has been canonically mentioned by one of the characters. Has the author (or the light novel) given any canonical reason for his teeth to be pointed, or is it just symbolism of him being like a shark?
I think Rin's teeth are depicted as sharp to give off Rin's attitude towards his former teamates Haruka, Makoto and Nagisa. If you remember during the series Rin had went to Australia to become stronger and faster in swimming. But a couple years later even though he put so much effort in whilst in Australia he still couldn't beat Haruka.
This is probably the most accurate time to say when Rin became more aggressive and serious. I think his sharp teeth are suppose to tell the viewer that he is serious and gives off his more aggressive personality and persona.
This is just my impression though. I dont actually think they made his teeth sharp for an actual purpose rather than to display his change from when he was a kid to when he lost and decided he had, had enough of losing to Haruka.