I am currently playing a paladin in another adventure path and the moral dilemma has been a compelling RPG hook. Although I do not advocate a GM targeting a specific player/character, there are times that a GM must respond to a character who is running amuck, so to speak.
That said, one of my frustrations as a player in this campaign is the number of foes (demons, summoned fiendish monsters, etc.) with 'smite good' has really hobbled my character's effectiveness in many fights. Almost any full round 'smite good' attack is enough to drop my character to single digit HP, rendering the character far, FAR more cautious in the remainder of the battle. A little humility and reminder of character mortality is a good way to inspire a more calculated play style. And before I get any critiques on the character build, we are using standard PFS rules for stats and HP.
Paladins radiate an aura of divine grace that makes them easy to identify by their alignment. Unless the player has specifically built their paladin to mask their alignment it is fairly difficult for them to avoid spells like Detect Good.
As for the looting vs. robbing argument, if a foe surrenders, the paladin is honor bound to accept their surrender, and they are also honor bound to protect their new prisoner's life and wellbeing. No turning them over to a torturer for interrogation, no execution before a trial, no releasing them unarmed into a wild and savage environment, no tossing them off a ship at sea, etc. Taking their equipment serves to protect the party and bystanders from potential harm during an escape attempt, but engaging a foe with the intent of taking their stuff is very in-paladin like. Taking equipment from prisoners that the party cannot use to sell and distribute the coin back to the party is little more than robbery and fencing the goods; the paladin should be shocked and appalled by the dirty money. If the paladin of the group is engaging in these activities, or ignoring/condoning these activities, they are straying into the deep end of the alignment tool.