Felicity says one of the Aldermen has a pacemaker and they can locate it if it is remotely programmable. Then Capt Lance says it needs to be recharged or they will have one less Alderman. At this time there are no rechargeable pacemakers, and current pacemakers do not have GPS built in. In order to remotely reprogram a pacemaker they must be near the device (with-in 75') that is accessing the programming. The only way to track a pacemaker is if they have the app on a smart device and then you would be locating the smart device, not the pacemaker itself.
At 10:39, there is a Half Moon at Nanda Parbat, but in the next seen, at 15:11, it is a full moon over Starling City, where it should have been previous night at most. About 7 days moon time passed between successive scenes.