Continuity mistake: When Claire is in the Captain's quarters, the locker falls open. As the camera pans up and left across the inside of the door, it slowly passes a photo of Cmdr. Winters in front of a banner that partially reads 'Welcomes Sinatra', and to our left is Frank Sinatra partly shown in the photo. Moments later, Olivia is looking at that same specific photo, and in close-up you can no longer tell who's at the left side (obscured by a hanging jacket) and the banner now reads 'Welcomes Goodman'. (Apparently there was a 'rights' issue that arose during filming that forced a switch to Goodman's name and music, and the earlier Sinatra shot was used in error.)
Continuity mistake: When Claire enters the Captain's quarters, she glances in to see the white desk is very well lit, and his Patrol Log is placed on top. To the left of the log is a brown cup and there is nothing between the log and cup. Seconds later, when she is looking down on the desk, the lighting is extremely dim, and a pen has appeared between the log and cup. The log is also in a different position (further away from anyone that sits at the desk) and Claire has to pull it closer to get it to the spot that it was at when first seen.