'causing injury' is an interesting thing to prove, since without the sperm the girl would not exist. Conflating the parties involved with the transaction being made (one of the parties _is_ the transaction) is sure to throw a monkey wrench into liability laws. This should be fun.
I'm not a judge, but if I was I would sidestep the whole issue by throwing this out because the girl has no grounds to bring a suit: her mother does. Then it falls neatly back into existing legal frameworks: did the sperm bank fulfill its obligation in the transaction?
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On further reading..
"..under a product liability law more commonly associated with manufacturing defects"
Damnit where is the wikipedia of law? Can't they at least _name_ the law, "US Code Title XII Section 5 Subparagraph Whatever.."