Plot hole: Anderton's wife gains entry into the jailhouse using her husband's eyeball - but he's already locked up inside, so his eye would not still have access to enter as it pleased. Any place anywhere that would have any sort of security system requiring anything from a simple passcode to a card key to a retinal scan, would immediately delete the user in such instances from all rights. And would also certainly report on any attempted use of such (retinal scan, pass code, whatever).
Plot hole: When Witwer invites Burgess over to discuss the problem of Anne Lively's murder, he gives Burgess Anderton's gun saying "We recovered that from Leo Crowe's hotel room", yet making no mention of why he is showing the gun. It makes no sense why he would bring the gun or give the gun to Burgess seeing as he would have to remove it from the evidence of the murder. There was no important evidence regarding the gun he would need to show Burgess and only seems to serve the plot (as Burgess uses the gun to kill Witwer at the end and the blame goes on Anderton). What complicates the matter further is that Witwer knows someone in the Pre-crime division was behind Anne Lively's murder, so to give a person who could very likely be involved in the murder a LOADED gun seems a little risky and unnecessary.