Plot hole: When Brian is on the boat, we see 3 girls from the auction being ushered into the sheikh's stateroom. He eliminates all the bodyguards, the last of who is the leader with the knife, and who is the only person who knows which of the girls is Kimmi. When Brian enters the stateroom, the sheikh is holding her at gunpoint. How did he know she was Brian's daughter?
Suggested correction: This is a question, not a plot hole. It is possible the man who bought Kim at the auction had to explain to his boss, the sheikh, why he bought her. He probably told him about the troubles he has had and the possibility that this man is still searching for his daughter, the girl in front of him. Hearing the fighting going on the sheikh correctly assumes this is the same man and tries to use her as a shield against him when he enters and threatens her with a knife.
Don't think so - lot of probable's. The Sheik's right-hand man would have assumed Brian was dead as St Clair's men had captured him, but he spotted him on the boat and only told his boss he would 'kill the dog', not which girl he had come for. Agree correction - she was held by knife-point.
He bought a girl he was not instructed to buy, for a lot of money. Of course he had to explain that to the Sheikh.
Not a plot hole, not even a contrivance. The sheik just grabbed whichever girl that was with him. It didn't matter who she was, it was just a case of "let me go or 'll kill this random, innocent girl." The fact that it was Kim was a simple coincidence (1 in 3 chance).
Suggested correction: There's nothing to suggest that the sheikh did know. He just grabbed one of the girls to use as a "shield". It didn't matter to him if it was Brian's daughter. We only place significance on the act because we know it's her, and humans like to find meaning in things.