Here's a list I made of spells I think we might see as we level up the rest of Blue Mage.
Brainjack (Long-Armed Chariot) - About as useful as the BRD charm spell...
Level 5 Petrify (Ahrimans) - Inneffective on NMs.
Hurricane Wing (Fafhogg) - Flash type blind and AoE Wind damage, similiar to Actinic Burst but with small damage too.
Earth/Aqua Breath (Aspid) - Next tier breath spell for BLU, 2/3rds based HP instead of 1/2th with Heat Breath.
Flame Armor (Behemoth) - Let's face it, they won't give us Meteor, and if they give us Thunderbolt, it will be trashy.
Diffusion Ray (Chariots) - Another option for a higher tier breath spell.
Roller Chain (Ramparts) - AoE Damage and Bind
Restoral (Gears) - Pollen-like spell for Cure V+ potency
Lava Spit (Cerberus) - AoE Fire Damage
Slaverous Gale (Sandworm) - Conal frontal damage
Tail Lash (Amphipteres) - Physical damage, higher when behind the monster
Heliovoid (Vampyr) - Absorbs a random stat from target monster
Sinker Drill (Acrolith) - Single target physical damage
Fossilizing Breath (Khimaira) - Like Level 5 Petrify, unlikely to land on many things
Electrocharge (Spheroids) - Like Regurgitation, a useful Thunder-based nuke for BLU
Pyric Bulwark (Hydra) - High physical resistance(phalanx-like) for a very short duration
Cackle (Dvergr) - MAB, MACC, and MDB down to target monster
Asthenic Fog (Yovra) - AoE Drown, like Cold Wave
Could learn all 5 of the Simulcra statue abilities as well:
Seismostomp - AoE Damage and Stun
Lead Breath - Cone Attack Weight
Numbing Glare - Gaze Paralyze
Tormentful Glare - Gaze Curse
Torpid Glare - Gaze Sleep
With the release of the CoP area level cap, I think we'll have access to empty abilities too:
Quadratic Continuum (Gorget) - 4-hit physical attack
Murk (Cravers) - AoE Weight and Slow, like Mysterious Light, but with slow effect too
Empty Seed (Memory Receptacle) - AoE Knockback and Damage
Vanity Strike (Seether) - Yet another stun ability for BLU
Winds of Promyvion (Thinkers) - Erase
Vanity Dive (Wanderers) - Single target damage
Auroral Drape (Weepers) - AoE Blind and Silence
Maybe even some Ultima and Omega spells >.>