If I cast Inquisition of Kozilek, and my only target is a Loxodon Smiter, do I have to make my opponent discard the Loxodon Smiter, or can I "fail to find" just as I would if i were searching my library?
You can "fail to find" a card, but only while explicitly searching someone's library or hand. In the case of Inquisition of Kozilek, you are not "searching" the zone, so you must choose a card if a valid choice is available.
Per the comp rules, "fail to find" is specific to searching a hidden zone:
While the hand is still considered a hidden zone even when it is revealed (CR 400.2: "Library and hand are hidden zones, even if all the cards in one such zone happen to be revealed"), Inquisition of Kozilek's instructions say to choose a card from it, not search for one. Thus, you must follow the normal rules: which is to carry out as much of the actions as possible.