A few things I've noticed about Quests
that are odd:
You can click the alert box away in the big circle… but only two times. If there are more than 2 quests that open at the same time, after two touches of the circle, you must then touch the Continue button for the subsequent alerts
Even if you click Begin Quest (bottom right) on a quest initial screen/description, when you return to the Quests tab, you see the description, not the gallery/list of Quests. The only way to get back to the gallery/list is to use the back button on the Quest description page (even if the quest is completed). I think that returning to the Quest should take you to the list-- otherwise it becomes confusing because your Quest may actually be completed (but you'll still see that initial description screen until you touch the back button).
If you return to look at a Completed Quest in the Quest tab, the bottom button (lower right) still says "Begin Quest” (even though the quest cannot be re-begun)