The Mishnah in Megillah (2:2) says that one who reads the megillah while semi-asleep ('מתנמנם') is yotzei. The gemara comments(18b):
מתנמנם יצא וכו': היכי דמי מתנמנם אמר רב אשי נים ולא נים תיר ולא תיר דקרו ליה ועני ולא ידע לאהדורי סברא וכי מדכרו ליה מידכר׃
What's מתנמנם? Sleeping, but not sleeping, awake, but not awake. If you call him, he'll answer; he can't do a sevara, but if you remind him, he'll remember.
This may imply that one does not need to be focusing very well to be yotzei. Where is the cut-off where one is no longer yotzei? If a person is daydreaming, but he hear's the words in the background, is he yotzei? What if he's looking at something else, e.g. his cellphone? This is also relevant for other areas where you need to listen to be yotzei, such as Kiddush on Friday night.