Plot hole: The villain's plan can work and fool the judiciary system because of extraordinary coincidences out of his control. He needs to steal the gun of his wife's lover in broad daylight without employing any modicum of stealth; he needs said lover to be the particular negotiator assigned to that case. He then needs the two agents standing by the door to be unable to hear any part of the confession he spews out, and to be absolutely sure that the detective has no recording device or radio contact throughout the ordeal. Not just that, but the spry septuagenarian also switches guns with cat-like ability - Nunally left his gun by the open door, where the other two agents are waiting. So the other two policemen had to be deaf and blind for his plan to work. He does not even have any time to switch guns with Nunally from our perspective as viewers; for the tiny five seconds when he is off camera and out of Nunally's direct eyesight, he is taunting him while supposedly moving around the large entrance to grab the gun.
Other mistake: The Italian version redubs the antagonist as "Thomas" and "Tom," localizing the movie title to "The Thomas Crawford Affair," in an obvious attempt to capitalize on the fame of the cinema classic "The Thomas Crown Affair." However, end credits (and obviously the police report) still list Hopkins' character as Ted Crawford.
Answer: Crowford (Hopkins) shot his wife with the gun that belonged to Nunally (Burke), but switched it with his at a moment of Nunally's distraction. The gun that the police mistakenly collected was not the murder weapon. This was a key plot point. Crowford goes on to gloat about it near the end of the film, saying the one piece of evidence Nunally needed was on his hip the whole time.
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