My BLU is currently lvl.28, and I'm almost caught up with all my spells, but some spells (i.e., Healing Breeze) took me several hours to obtain. I would often question whether or not I was doing something wrong, but I had no way to be absolutely sure.
Perhaps an Learning gauge would be helpful. If one defeats an enemy that has used a learnable spell, that spell's learning gauge goes up by a random percentage. The higher the BLU's Blue Magic skill, the more likely it will be raised by a higher percentage. This could potentially help BLU's by cutting down on the number of mobs they have to go through in order to learn a spell (if their skill is high), and it would also give a way for BLU's to check their progress on learning a particular spell.
Just an idea, it could be awful.