Lie detectors do not work the way it was used throughout this episode. Only yes/no questions are asked, and lie detectors do not confirm when someone is believed to be telling the truth.
JT shoots his dart and hits Dana's picture in the mouth, however the camera immediately cuts to a wider shot of the fire place and you can see his dart is missing.
Cody clearly sprays the fire extinguisher above the flames so the fire would not have gone out within seconds.
When Cody is playing records as a DJ in the diner, the turntables do not have an adapter for the 45rpm singles. As a result the larger hole causes the record to spin with a wobble which would distort the sound of the song.