So first a disclaimer: Yes i am aware that the schools of magic in the Elder Scrolls are an arbitrary system that change based on the teachings of the magic authority in a province.
Now that that is out of the way (this was a grammatically correct sentence but it is still strange-looking when written) we can move on to the topic.
In Skyrim the schools of magic have shifted a slight bit from their previous iterations as well as adding "new" spells and deleting an enormous amount of older spells. My issue is with how certain spells in this iteration are categorized in what (to me) seems incorrect. For example the Muffle spell is placed in the Illusion School but based upon how it works it seems to me that it should be in the Alteration School as it "manipulates reality" to remove sound from the caster's footsteps while Illusion is intended to trick the mind of someone but if you cast this spell on yourself then how can it affect absolutely anyone you encounter? It does not constantly drain magic so it isnt an adapting effect and yet it apparently affects everyone in Tamriel. I suppose the same can be said about Invisibility and if you want to add that to this theory then by all means go ahead.
Some others i feel are misplaced: Paralysis seems like an Illusion spell as it would make sense to assume that you can "trick" someone into believing that they cannot move where if this is truly Alteration then you are manipulating reality within or around their body to stop them from moving...which doesnt seem like a sensible spell since with that same idea you could just encase them in stone or something.
Ward spells are in the Restoration school but nothing about them really fits with how Restoration feels (at least to me but maybe im just odd). In my mind it seems like creating a barrier of anti-magic out of nothing is Alteration (or Mysticism as i would prefer).
Sunfire spells (added with Dawnguard) are under the Restoration tree and they are described as being the same energy from the sun placed into a spell...which logically in the Elder Scrolls universe means they are a pure-magic spell which still feels like it fits into Destruction (or Mysticism) as harnessing pure magic isnt related to Restoration at all as far as i am aware. I do however believe this one is thrown in because Turn Undead is in Restoration now as since Sunfire is only useful against Vampires (who are Undead) that Bethesda was just like "whatever".
Detect Life/Dead are in the Alteration school but they are in no way a manipulation of reality as they dont change anything especially since only the caster can see the effect. The detect life spell was originally in Mysticism and since it's unwanted removal Alteration is where they stuffed it but that is the least-likely home for it (other than destruction). I would have opted for Conjuration since Soul Trap has been moved there (seeing the souls of the living) but only for Detect Life. Detect Dead may have been more befitting in Restoration but i dont really see a good place for it.
Command Daedra seems like any other Command Spell from previous games and would be under Illusion rather than Conjuration as it does not summon anything into this realm and it doesnt bind a Daedra, it just temporarily commands them like an Illusion spell. Although i will say that as far as i am aware even an Illusion spell shouldnt make a summoned (bound) creature attack it's caster because that breaks the rules of binding however this idea also applies to the Conjuration spell as there is nothing that states that it changes the rules of binding.
Flesh spells are in the Alteration school and going by their names they make sense but what they actually do it create a magical shield around the caster but this si the same thing Ward spells do but against physical harm. Now i dont think this should be placed somewhere else but that Wards and Flesh spells should be in the same shcool (also that the flesh spells should look like their names ie coating you in iron or ebony)
Candle/Mage Light are spells in the Alteration school but they dont involve manipulating anything, they create light from nothing which is more like Illusion (or Mysticism) as the light cannot be touched so it is reasonable to think that it is not real and is instead an Illusion the caster places on himself to see in the dark but this one is kind of wonky either way
Equilibrium is an Alteration spells that transfers your life-force into magicka which is kind of hard to categorize but i would say that since it deals with your life force it should be Restoration especially since it does not involve much manipulation of reality.
Other than this i still believe that Mysticism should have remained a school of magic as all of it's spells still fit better into it than their "new homes"
So discuss...
ADDED: Clairvoyance should not be in Illusion...i cant even fathom what the logic with this one is. Seeing the path to your goals (or the future going the by the actual definition of the word) isnt related to tricking yourself at all. Mysticism is best for this but they just had to streamline the game