Each patch will update and add to the abilities a Blue Mage can acquire.
The limiting factor to Blue Mages is found in the distribution of "Set-Up Points" gained with each level. If, say, Spider-Web costs eight Set-Up points to "equip" as a spell from the list of available spells, and the Blue Mage only has 16 Set-Up points, then if Spider Web is equipped, the mage will have eight Set-Up points leftover to use on other abilities.
Spells and Set-Up points will increase in quantity with each level.
The effectiveness of Blue Mage magic depends on what spell you acquired from what type of mob. For example, if you acquire Helldive from an Akbaba, and try to use that move against a slime, since birds are weak versus slimes, the move will also be weak.
Some blue magic can be used in Skillchains, and can also be used in Magic Bursts.