Plot hole: Batman finds at Belson's home a handwritten list of substances needed for a transplant. Why would Belson, a medical authority in the field that knows those things thoroughly, even write a list down? If it's for Freeze to procure him the material, why would it be at his house and not with him, and when did he even have time to be at home to do that, since he has been kidnapped by Freeze when he was driving on the outskirts of Gotham and taken to the oil rig? If he had time to go home, he at least would have changed clothes, he's still in the tuxedo he wore when he was kidnapped the night before.
Plot hole: There are 17 possible donors for Mrs. Fries. Of all of them, instantly and with no explanation, the doctor chooses Barbara Gordon. She was not the first alphabetically, from the phone call they find out she has a roommate, a boyfriend, she is out for dinner at the moment and is going out of town and of course, REALLY huge warning sign, she is the daughter of the police commissioner (hard to ignore that in Gotham, and Freeze certainly knows him first-hand!). There's no reason why to kidnap her, plenty of reasons not to, and zero reasons given why they did not try any of the other 16 names on the list.
Suggested correction: They did explain exactly why they picked Barbara. The names on the list weren't all perfect matches. They were looking for someone "who's approximately the same weight, height, and female." When he sees Barbara's file, she's a perfect match. The fact that it's Jim Gordon's daughter is of no concern to them, assuming they know it's his daughter since Gotham is said to have a population of 10 million.
You are quoting the movie but then describing something radically different from what is shown (which I understand, since what is shown makes little sense). The list of 18 people (one being Mr. Freeze's wife) is the one that appears exactly *after* he has refined it for "approximately the same weight, height, and female." Everyone on that list should be a perfect match, otherwise there was no point at all in showing him writing F, 5'2", 116 lbs, AB Negative in the search fields and get search results for it. If it's not, he has no way to tell at first glance.
Plot hole: Mr. Freeze's old pal Dr. Gregory Belson needs to search for a compatible *organ* for Freeze's wife. He's trying to go through the proper channels at first, and search for, in his words, "available organs" and "deceased donors." The weirdest part about it is that he's searching the blood donors database. Why would the blood donors database have that kind of information? (00:19:20)
