A final note before I let this thread die. I spoke with the player yesterday at the beginning of our game session, and we came to a conclusion about how the character should be behaving. We disagree as players on how Lawful Good should act in some situations, but we both have a consensus on how the >character< should be acting, and that is what is important. I believe that alignments, like religion, are very personal and dynamic, and I am not the kind of person to push my views on others. But he sees where I am coming from and agrees that I have a valid point.
I also issued a warning to him stating that although I wasn't going to make his character fall, if the behavior continues he very may well fall. He agreed that his character acted irrationally and that if the behavior continues he deserves punishment.
"I am Lawful Good and you are not so I will kill you," was the standard description of "Lawful Stupid" behavior back when I was in high school.That seems to be how the OP's paladin approaches the world.
This. Slitting the throat of a bound and unconscious enemy captive is a Chaotic Evil act. As is breaking the reverie of a shaman by beheading him. That Paladin is committing evil acts and no longer deserves his rank, station, and standing with his God. Simply detecting evil on a creature is NOT justification for metering out blind justice as he sees fit. The Paladin should either fall to Anti-Paladin (let's face it, he's using the "greater good by ANY MEANS NECESSARY" approach, therefore corrupting himself that far. This reeks of classic villain syndrome.) or at least be stripped of his Paladin abilities and become a Fighter.
If he does it a third time, consider a forced alignment change as well.
Bottom line: You are in control of the consequences. Unless he's completely new to the game and the class, he's Paladining incorrectly and needs to be set back on the right track or shown other options.