There is no time limit for the escort quest, but if you complete any of the 3 main plot quests that give you an invitation to the castle (the army quests, the plague or the old duke's murder) the healers will move on their own. If you had not healed the 2 soldiers in Aleroth by then, those quests will also fail.
If you skip restoring Mardaneus' sanity (by clearing out the catacombs), his status will get reset (and the related quests will fail), but I am not sure exactly when (somewhere between getting an invitation to the castle and scrying for the human council member).
There is only one specifically timed quest; in Verdistis, if you agree to commit arson, you must do so that game day or someone else will get to it first.
