Scott, this was a good question!
This was a subtle bit of dialogue as Spock records the Captains Log and I can see missing it! I listened to the episode and I heard it. Not to check, but I wanted to hear it said in the episode and I can see how I missed it!
This was the forth production episode filmed. I can see it being a mistake at this stage. But I wondered if it was a mistake at all. Perhaps it was meant to mean the second officer behind the Captain. I wonder if the Navy calls the XO the Second officer and not the First Officer? I'm thinking of Crimson Tide and the exchange between Gene Hackman's character of the Captain and Denzel Washington who was the XO. And he's second in Command, IIRC.
Out of curiosity, I checked the Star Trek Memory Alpha wiki to see if they noted this and they didn't. Normally they point out these little glitches.
(By the way, don't read anymore of that Lost thread! I hate to see the end spoiled for you!

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