Let's say that a Paladin is fighting against an invisible opponent. Can they target it with their Smite Evil ability, even if they have identified what square the enemy is residing in? The particularly confusing part lies in the "the paladin chooses one target within sight to smite" of the abilities description. The Paladin might not be able to actually see their invisible enemy, but they know what square they're in and, presumably, it is within their sight.
You are correct. The only restriction on what creatures can be targeted with Smite Evil is that the paladin must be able to see the creature to be targeted.
Another way of phrasing that restriction would be to say that the target must be within line of sight. The line of sight rules state:
A line of sight is the same as a Line of Effect but with the additional restriction that that it is blocked by fog, darkness, and other factors that limit normal sight (such as Concealment).
The invisibility rules say that, when attacking an invisible creature:
the invisible creature still benefits from full concealment
I think it's pretty fair to say that, based on these rules, a paladin would not have line of sight to an invisible creature, and thus wouldn't be able to target them with a smite.