Stupidity: Lecter fires the first bullet to alert the police that something is up, and the lift goes up, then comes down. Now in all this, only 6 or 7 go up the floor where Lecter was. Why aren't police sent in groups to investigate every floor? Lecter could have been anywhere, instead there are about 30 police huddled on the lobby floor.
Stupidity: Clarice enters the ward with the most dangerous inmates, which is guarded by at least 2 male nurses and an officer, with CCTV and through 2 gates with bars that let the sound out perfectly. Before she enters, Barney the nurse even tells her he'll be watching, and Lecter is obviously the most important patient of the very small wing of the hospital. Clarice stays there barely a couple of minutes; the inmates begin to make a big ruckus, screaming wildly, but there's absolutely nobody to be seen at the gate, where everyone within earshot of the screaming patients would at least peek. Especially counting the fact that she already broke the regulation about getting close to the glass rather early in the chat, which should have alerted the guards. (00:12:00)
Answer: Knowing about her past gives him an advantage in how he can manipulate her - he understands her fears, weaknesses, strengths, and so on. A psychiatrist normally deconstructs a patient's psychological make-up to better understand and help them, but in Lecter's case, he uses this knowledge against his victims. However, as he learns about Clarice, he becomes sympathetic and protective toward her.
raywest