Veil thickness/thinness directly relates to how well some Battle powers work.

VERY THICK VEIL:

Spellbane and Spell Evasion work very well, Discern Spell sucks (because the magic is weaker, and therefore harder to sense), magic items do not function properly. Portals don't work at all. Pouch of Nourishment, everfull skin, and chest of inebriation stop functioning completely. Magical transportation spells periodically fail (like word of recall, teleport, etc...). When using Potions/scrolls/wands/talismans you will occasionally "utterly fail to use" them. Conjuring servitors has an increased chance of getting a weak servitor instead of a strong one. When you DO end up getting a stronger one instead of a longer lasting one, the amount of extra mana you put into the conjuration is counted as less than it actually is (or perhaps the required amount for that tier of servitor is simply increased. Effectually, both work out the same. I.e. XXX amount of mana is no longer enough to get the strength of servitor you wanted). Spells that would normally benefit from Spellcraft are diminished in power, as if your spellcraft was lower than what it actually is (like a global anti-spellcraft effect).

Conversely, when the veil is "virtually non-existent" spells that benefit from Spellcraft are enhanced even more than they normally would be by Spellcraft (like a global spellcraft effect that also stacks on top of your current spellcraft benefits), meaning more damage, harder to save against, etc... Conjuring servitors requires less mana to get stronger servitors. The likelihood of getting a strong servitor vs a weak one will be higher. Sometimes when casting a spell, the air is filled with motes of mana, and the spell costs ZERO mana to cast. When using sleeks, you will sometimes get the benefit of the item without actually expending a charge. And sometimes you get extra effects, like Resist Energy in addition to the normal aura/shield/barrier. Spellbane and Spell Evasion start to suck big minotaur balls. Discern spell works much better (because the magic is stronger, and therefor easier to sense).

I think got most, if not all of it. If I left anything out, please feel free to respond and fill it in.

So yes, state of the veil has a MAJOR impact on game mechanics.