General Mechanics:
Controls:
A - Basic attack
B - Special attack
AB - Super attack (consumes 2 Red)
C - Block

Most characters have netural, ↓, and → variations for all basics, specials, and supers with air variations of each.

ex.
Taiga's move list


Recovery
Press ↑ while in the air after hitstun ends to recover control

Evade
C+left/right
Ground only
Hit box generally disappears during evade

Parry
Pressing block right before an attack hits will parry it. The defender will take no chip damage, lose no gauge, and have a few frames of invincibility. Attacks that have multiple hits may not be interruptable, even with the frames of invincibility.

Autoguard
Certain attacks (and bosses) have super armor for a certain number of hits before they can be interrupted into hitstun.

Levels
Determine gauge size. Nothing else.

Blue Gauge
Fills over time
Depletes on block or defensive cancel (below)
If blue is empty, then extra damage is taken when blocking

Red Gauge
Fills when attacking
Will fill over blue gauge
Normalizes towards half when taking damage (+ if < half, - if > half)
Depletes on supers (2 bars)
Depletes on offensive cancels (below)

Canceling
Almost any attack can be canceled. They can be performed directionally (double tap a direction/C+direction), normal attack to special attack, a normal/special to special/super, or super to super. Not all characters can cancel in every direction (most can't cancel downwards for example) and many characters have unique cancels (ex. Berio's forward offensive cancel creates a shield that bounces the enemy back)
There are three main kinds of cancels.

Free cancel
Uses no gauge.
Norma attack to special attack (or super)
Upward direction cancel off normal attack
C+↑ from neutral will perform a free (upward) directional cancel

Defensive cancel
Uses one blue gauge.
Backwards directional cancels

Offensive cancel
Forward directional cancel off any attack
Upward/downward direction cancel off a special or super
Cancelling from one special/super to a different special/super
Note: Doesn't include the cost of using the super, so offensive canceling into a super will take 3 red total

Damage Prorating
Damage lessens the longer a combo goes on
Damage greatly lessens once an enemy is in a down position (even if they are relaunched into the air from it)
Damage lessens the less life an enemy has left

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Character specific notes
(Just done off the cuff, may have missed something)

Taiga
B, AB can be continued by pressing B up to two more times after striking

Mia
Ground B attacks are determined by length of time button is held and angle of release. Angle can be changed after attack begins.

Lily
→B and →AB can be held to increase detonation distance

Berio
B, j.B, ↓AB can be held to increase length/power of effect
↓B, ↓AB and ↓j.AB can be aimed after attack begins
↓C creates shield (req. 1 blue, depletes blue while up and lasts until blue is empty)

Kaede
Can triple jump
Has a downward cancel in the air
When using AAAAA, final hit automatically jumps
Has ↑j.B and ↑j.AB
j.6B, j.6AB are multiple hit attacks. Continue by pressing B with the correct timing

Rico
↓AB super only available when summon is out
Summon slime with →C
Summon Necromicon with ↓C
Orders for summoned monsters given with C+direction
Summons cannot be dismissed. They must be defeated before a new one is summoned. There is no limit on summoning otherwise.
Directional cancels have no slowdown or other visual effects
Directional cancels free cancel into themselves
Cannot directional cancel while a summon is out

Nanashi
Head has an independant hit box when detatched (damage is only taken by body)
Many attacks change while head is detatched
When head takes damage, it cannot be recalled/picked up for a few seconds
Being on top of head when it is supposed to enter a stunned state (ie at end of some supers) will automatically reattach it instead
When head is detatched, ↓B, ↓AB creates an extra grave underneath head

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Route Mechanics:
Route is set at the start of chapter 8. You are given a choice of characters to ask out and whoever goes with you is the route you are on. There is an semi-enforced route order and only the routes that are unlocked will be available to ask out. However, girls may turn you down if you have not gotten enough points/cleared enough flags with them. It's definitely possible (probable even) to have enough points with multiple girls on a single playthrough to choose multiple routes from a single save. Mia is selected by choosing nobody.

Route unlocks are saved to the system data and can be accessed from any game. Completing a girl's route also unlocks her for use in battle instead of controlling Taiga. Levels are carried over in an NG+ when the game is cleared (any ending) but levels are NOT saved to the system data.

MiaC* -- Unlocked from the start
Berio -- Unlocked from the start
Kaede -- Unlocked from the start
Rico -- Complete Berio or Kaede's route
Nanashi -- Complete Berio or Kaede's route
Lily -- Complete Berio, Kaede, Rico AND Nanashi's routes
MiaB* -- Complete Lily's route
MiaA* -- Complete MiaB
Justice/Crea -- Complete MiaA

*Regarding Mia's route
Unlike the other girls, you cannot be turned down when selecting it for having too few points with her. Entering it without fulfilling the conditions for MiaB/A (completing Lily and enough points with Mia) just pushes you into MiaC. MiaC is not a full route and completing it does NOT count as clearing Mia in any way. Second, there is a normal end and a true end. The normal end must be completed before the true end is unlocked. You can simply save in the final chapter and then reload after seeing the normal end to see the true end.

The Justice/Crea route splits off at the end of chapter 7 instead of the start of chapter 8 (as far as the scripts and save files are concerned). If the conditions are fulfilled, there will be a prompt to begin it at the beginning of chapter 8. If no prompt comes up, you have failed to fulfill the conditions.

A quick mnemonic for remembering order is large breasts, small breasts, medium breasts. There is a much more specific reason they're grouped/ordered like that but it's quite spoilery.
NOT KIDDING WITH THE SPOILER HERE


Crea events for her route (Destiny Only):

Chapter 4, 2nd Free Action (Night) - Gate
Chapter 5, 1st Free Action - Gate (Choose not to bug Berio)
Chapter 5, 2nd Free Action - Gate
Chapter 6, 1st Free Action - Gate
Chapter 7, 2nd Free Action - Gate

ALL MUST BE DONE TO ENTER HER ROUTE.

No other requirements apparently, besides clearing MiaA.

I have no good idea how harem route is unlocked besides winning all the battles.

Bugs:

Imn's backdash is slightly glitched and will execute her summon's super off an HJC for no cost.
Demo: http://www.youtube.com/watch?v=NDGcH9RXZew
Demo: http://www.youtube.com/watch?v=ZcpjN8JmwhY
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Too many collisions simultaneously with a frozen sprite can overload the game and cause all projectiles to lose both substance and hit properties.
Demo: http://www.youtube.com/watch?v=bf1XYk8nHNs

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Possibly related, but I haven't been able to duplicate it, so I'm not sure WHAT this bug is exactly. It looks like the game tried to HJC from the offensive cancel and just putzed up Nanashi's head, resulting in the same error as the ice one above.
http://www.youtube.com/watch?v=KBE1SaIqwlE&#t=11m20s

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Guarding while jumping can have strange effects on momentum. Usually, it's just a very quick deadfall (which is probably intentional), but for characters that have a double jump, tapping block right after a double jump can cause them to rocket upwards. AI Berio tends to do this a lot for some reason.
Demo: http://www.youtube.com/watch?v=gtqsUzeCzGI
Demo: http://www.youtube.com/watch?v=PMlsZCJ6XEE

This was fixed for most (all?) characters in Xross.

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When you block, the screen locks for a moment (presumably during the parry frames). If you're moving fast/far enough and tap block rapidly, you can scroll yourself off the screen. Also note that things a little ways off the screen have wonky hit detection, so this could probably be even glitchier under certain circumstances.
http://www.youtube.com/watch?v=1ZcD3_E5YZc

Destiny voice glitches:

taig000000 is an empty padding file, but it's called in the game twice. Once at the start of Crea's route (stomach rumbling noise), and once at the end of Lily's route during the escape. The two lines are not even remotely alike.

Voice 3090030173 and 3090030203 are backwards in Destiny in Berio's route. They're the same line for both, just one has reverb since it's a flashback. I've gone ahead and swapped them back to fix it.

Voice samples 0065060009 and 0065060010 are identical files in Destiny (hospital in Nanako's route). They shouldn't be, but they are. There's nothing I can do since the right line doesn't exist.