When Jake returns to Jericho, he stops at Stanley's farm. Stanley greets him with a hug, pinning his arms. In a reverse angle shot of the same scene, Jake's arms are free.
The license plate on Jake's car disappears/reappears several times.
The vehicle that Jake drives, a Plymouth Road Runner, changes from a 1969 to a 1968. At the beginning it is clearly a 1969. After the accident, the views from the rear of the vehicle show it now has 1968 taillights.
(During the beginning credits) The first time we see Jakes car, it has no License plate on the rear bumper. A couple shots later his car mysteriously has a Kansas License plate on the rear bumper.
Ordinary everyday background radiation will cause a geiger-counter to click between one to three times a minute, yet the Sheriff's machines stay entirely silent.
An answering machine will not record dial-tone after a call has ended.
The cars would not function during the initial nuclear explosion. The Electromagnetic Pulse (or EMP), traveling from a nuclear blast at the speed of light, would paralyze not only the radios and TV's, but also vehicle magnetos, causing them to stall.
Although the blast from a nuclear explosion would travel rapidly through the atmosphere, the fluffy clouds continue to drift idly by at right angles to the impact, unaffected by the several tons per square inch pressure suddenly imposed upon them.
When he's driving out of town and runs head on into the station wagon, let's consider they're both driving a minimum 40mph toward each other. The last frame before they hot shows both cars o more than 20 to 30ft from each other. They will hit head on in less than 1 second. But somehow he's able to pull a 90° to the left and hit them at the rear of the Plymouth Road Runner.
The series take place in Kansas, but the mushroom cloud rises from mountains. Mountains aren't visible from Kansas.
Denver, Colorado is 175 miles from the Colorado/Kansas state line. It is highly unlikely that you would see a nuclear explosion in Denver from Jericho in NW Kansas, nearly 250 miles away.
Coming from Denver, Colorado or any other direction there are no signs (like the one in season one, first episode during the credits) that would have Kansas City and Wichita listed on the same sign. From Denver on I-70 you are more than 90 miles north of Wichita putting it completely out of the way of Kansas City. Hays, Salina, And Topeka are the control cities listed on I-70 before you see Kansas City if you are head east from Colorado.
Originally, Jericho is supposed to be in northwest Kansas approximately where Hill City is located in Graham County. When the mayor and other men are trying to decide who should go what direction to see what has happened elsewhere, a deputy is standing in front of a map on a wall. The map is a blow up of Ness County and Jericho is located where Ness City should be in southwest Kansas. To the north of Jericho there is a clear image of an airport symbol, it says "Ness City Municipal Airport" when it should be Jericho.