Wow, eight pages of thread for an incident that covered maybe ten minutes in our game.
Now, as the DM for the paladin in question, I didn't see the character's actions as a major infraction. In fact, I didn't even think it worthy of a discussion. But, that said, there are some points that I don't think have been brought up.
1. The paladin expressed her concern that the orc, if set free, would simply join up with another band of marauding humanoids and continue to wreak evil. Now, this is a very logical assumption, and as the DM, I can tell you that's exactly what would have happened. Since there was no time for a trial or anything formal, an execution was certainly not outside of her alignment or code.
2. The orc was offered an honorable death. He refused and fled. The paladin saw this as an act of cowardice further demonstrating that not only was the orc evil, but that he lacked honor. Now, I agree that this is act is more LN than LG, but still I don't think its amounts to a major infraction.
3. The orc was not tortured, he was not "back-stabbed", he was, in fact, dispatched with a single blow from the back of a charging mount. I would think that this kind of death would be almost instantaneous, and if we are talking real world here, probably more merciful than an execution, which would often take 2-3 strokes to sever the head.
Now, nothing I have said above invalidates any of your arguments regarding the paladin code, as this is a pretty subjective matter. I just wanted to give you all the skinny on what was actually said and done.
Thanks
BD