Mahouka Koukou no Yuutousei

You missed one more, ahahah. Tatsuya is being limited by Miyuki, so a 5th "hidden potential" is actually the fact that he's being sealed by Miyuki.
The seal is suppressing his psion count, as well as Miyuki's. Regarding what you listed as his first hidden potential - "decomposition magic", wasn't he unable to use trident (the 3-step technique, not the CAD) properly when sealed?

More on decomposition magic - regarding his strategic-level classification, if he's given Third Eye to use, then he can use his Material Burst as well. Mn, but that's the kind of thing used to level cities from very far away, not duel senpais at school lol.

His Elemental Sight isn't something he learned from Yakumo. Moreover, ninjutsu is counted as an ancient magic in this series, so really... even if it was ninjutsu, it'd still be magic since it involves reading the eidos lol.

No, that skill of detection came from his training in Ninjutsu, not because of magic.

He can sense and discriminate all particles that surrounds him in very vide area. That basically means than you can't ambush him in any way. I don't know details but I am pretty sure he is comprehending his world much like Neo saw The Matrix- Inside out.

From what I've read, there's 3 powers he's specialized in, 1 natural and 2 artificial.
1. Decomposition magic - This seem to be Tatsuya's own magic, which makes him a Born Specialized magician? And thus explain why he's so poor at doing normal magic.
2. Flash Cast - One of Yotsuba clan's secret magic. This thing is responsible for his lack of emotion. By carving an area in your mind where the full
http://www.batoto.net/read/_/154085/mahouka-koukou-no-rettousei_ch14_by_mangaholic/22
Basically he can go to that magic is constructed step in this diagram.
3. Restoration - He basically can copy-paste a 'normal condition' self over whatever his current injury is, and this work automatically if he lose conscious. Combined with Flash Cast it makes for one immortal bastard.

However, all 3 of these are secrets (first one being a weapon-of-war level power so if it's known to publics that he has it he'll be under constant 'protection', 2nd is Yotsuba's secrets and they don't like revealing it, 3rd is apparently even more shocking to be revealed than 1st but I forgot the reason)
So his arsenal is VERY limited.

His magic is decomposition after all.

technically he's not a siscon since he was programmed that way, though you can also say he was programmed to be something like a siscon.

Tatsuya moping the floor with Hattory. Again.