There are I believe three monsters that you need to defeat before moving on with the storyline on the Floating Continent to make them available in the Veldt (I know one of them is Grenade).

Make sure to get the Water Rondo dance for Mog, you need to fight in either the Serpent Trench or the Lete River to obtain it.

Make sure to purchase Golem and Zoneseeker at the Jidoor Auction house if you haven't already. Besides teaching useful spells, these two Espers have summon effects that will be useful throughout the entire game. Zoneseeker in particular will be especially useful from now on since enemies use increasingly more powerful spells to nucleify you with.