Continuity mistake: When Marco is in the library searching the internet for information about the scientist, he isn't wearing headphones. Then he notices the security camera recording him, and in the next shot, from the camera's POV, he's wearing them. When it cuts back to 'our' regular view they're gone again immediately, and he puts them on to listen to the computer.
Continuity mistake: In the scene when Liev Schrieber is with his mother before they go out to the party, she kisses him, than starts to lean forward to kiss him again. But when the camera cuts to the reverse angle, she hasn't moved an inch. It's as if she lunges back to her original position.
Chosen answer: The tattooed woman was something that they all dreamt about. She was significant to the capture and the tattoos stood out among all of the other arabs.
Toolio
I always felt they were just there to cause confusion. If they started to remember the image of the Arab woman/ women would sound and look crazy trying to explain. However later in the movie when they shoulder flash backs the women were not there and Shaw choked out that other guy but, early the Arab women where there, and he had plastic on his face choking him out. So, all the memories are mixed up.