I’ve got three - as far as I see, none of them have been mentioned before.

1. The Trio’s names

Harry Potter = Otter

Ron Weasley = Weasel

Hermione Granger = Ermine

Ron is a pureblood, who shares the name Weasel with his whole family. Harry is a halfblood, who inherited the name Otter from his wizard father, but doesn’t share the name with his Muggle relatives, the Dursleys. Hermione is a muggleborn, who got her animal in her first name, and doesn’t share it with her parents. The otter, the weasel and the ermine all belong in the same family, called mustelidae, which comes for the Latin word for weasel. Both Harry and Hermione ends up marrying into the weasel family.

(Image source: Wikipedia)

2. Quidditch parallels the Battle of Hogwarts

There’s a big fight going on. People are scoring goals, trying to knock out their opponents and keeping their own players safe. But what really matters is one player on each team: the Seekers, or Harry and Voldemort. They never truly participate in this big fight. The Seekers are searching for the Golden Snitch, Harry’s searching for the last Horcruxes, Voldemort’s searching for the Elder wand, and then waiting for Harry in the forest.

And Harry, with the unerring skill of the Seeker, caught the wand in his free hand as Voldemort fell backward, arms splayed, the slit pupils of the scarlet eyes rolling upward.

Harry and Voldemort, or the Seekers, are the only ones who can beat each other, not because of destiny, but because of unwritten rules. The game only ends when one of the Seekers beats the other - the Battle of Hogwarts ends immediately after Voldemort’s death - and unless the rest of the people on side have performed very badly compared to the other, their side will win.

3. The colors of their eyes

• Red is the color of Voldemort’s eyes, Harry’s Hogwarts house (Gryffindor) and Harry’s signature spell (Expelliarmus).
• Green is the color of Harry’s eyes, Voldemort’s Hogwarts house (Slytherin) and Voldemort’s signature spell (Avada Kedavra).

Red and Green are also opposite colors on the color wheel.

Of course, this is ruined by the movies, where both Harry and Voldemort have blue eyes.