Steve Wagner hands a box of laser pointers to a young girl who grabs one and passes it to the student behind her. In the next shot she is passing the box back to the student behind her again.
When Monk stops the plane from taking off, you can tell from his shadow that the sun is high in the sky. By the time Wagner is removed from the cockpit and arrested, the sun is setting. That much time shouldn't have elapsed between the two events.
The astronaut is visiting his ex-girlfriend the day before he is launched for a week in orbit. But in reality, astronauts who are bound to be sent into space are secluded from the outside world for a distinct period of time to prevent contamination or illness.
The astronaut in this story also flies as a test pilot. In actuality, while astronauts have often been test pilots prior to joining NASA, they don't continue in the role - being an astronaut is a full-time job.
One of the airmen in the hanger incorrectly called the rockets missiles.
As Monk steps in front of the F-22 Raptor, you can see the vehicle towing the Raptor leaving the camera frame. The shadow of the vehicle or crew can be seen in the subsequent scenes.
An autopsy should have determined the victim had not eaten for days before her death.
As part of the way Mr. Monk discovers that the doll contains a garage door remote, the plot requires the remote to open all garage doors it comes in close proximity to. In actual fact garage door remotes are coded to a particular series unique to one door. Unfortunately this was inconvenient as it would have made it impossible for Mr. Monk to discover the remote inside the doll.
When addressing the class at Career Day, Steve Wagner (Jeffrey Donovan) says he flew the shuttle over Florida and splashed down in the Gulf of Mexico. Space Shuttles orbit the earth from west to east, so he would have had to fly over Texas to get to the gulf, not Florida.
Wagner tells the class he will soon be test-flying the F-22A. The episode aired in March 2006, while the F-22 entered official service in December 2005.