Mind's Dilation

If you don't cast the card, perhaps because you choose not to or because it's a land card, it remains exiled.

If the card has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If you cast the exiled card, you do so as part of the resolution of Mind's Dilation's ability. You can't wait to cast it later in the turn. Timing permissions based on the card's type are ignored, but other restrictions (such as "Cast [this card] only during combat") are not.