Corrected entry: Towards the end when the helicopter is flying past Big Ben you can hear it chime. However, the time shown is 12:35 so this is impossible. (01:38:51)
Corrected entry: When Cage and Rita get past the beach and plan to get a car, she goes for the minivan, and breaks the window of the driver's side door to get into the car. In multiple scenes the window is undamaged. When they drive out of the park, you can see the open window.
Corrected entry: When the helicopter arrives at the Louvre, it totally destroys the glass pyramid. A few minutes later as the camera leaves the scene, the pyramid is totally intact.
Correction: The pyramid gets destroyed on one side, then the explosion blows the glass out leaving the metal frame - this is what we see.
Corrected entry: There is no reason why Rita and Cage would try to escape the building after receiving the device from the general. Cage could have just simply stuck himself with it in the general's office and get the right vision without risk of being shot at and have his blood replaced, about which Rita warned him several times. After receiving the vision Rita could have just shot him and up the beach they go again towards the Louvre. The general would have not intervened, as at that moment he believed him.
Correction: The device is untried and they don't know exactly how it will work on Cage (ie. if it will incapacitate him) or how long the process will take, so it's not a good idea to try to do it in front of the general, who might need only a single moment of distraction to call for backup, or to disarm Rita and kill them or take them prisoner. It would not be wise to suddenly trust the general completely just because he finally gave them the device (at gunpoint, remember). You're also incorrect to say that 'at that moment he believed them'; he actually just wanted them to think he'd taken their side, so he could have the soldiers attack them as they left... The same thing he did to Cage during the blackmail scene.
Correction: Big Ben wasn't ringing because of the time; it was being rung to signal the end of the war. There are a lot of bells being rung (church bells, other bells) for the joyous occasion and Big Ben was one of those bells.