After Shawn and Gus visit Henry to give him the plant, they walk along a pedestrian path. A seagull takes off from the ground and in the last second of the close up is at the height of Shawn's head and the camera immediately cuts to a distance shot but the bird is completely gone.
Jessica tells Gus that the astronomers had discovered an extra-solar planet six months earlier and that they were checking their data and waiting for the planet to complete its orbit. However, real astronomers would have waited six months not for the planet they were observing, but for Earth to move exactly half of its orbit around the sun. This makes the difference between the places where the observations take place as far as possible, allowing the most accurate calculation of the new planet's parallax. Parallax is the method by which astronomers can calculate an extra-solar planet's distance from Earth using the diameter of Earth's orbit, the angle at which the star is observed, and trigonometry.
The lock on the observatory door is a deadbolt, which is impossible to unlock in the manner Vernon is shown to have done.
At the beginning the date 1987 is shown, and Shawn is buying candy bars. In one shot the Butterfingers behind him has the Nestle logo on the wrapper. Nestle didn't buy the rights to the Butterfinger candy bar until 1990.
When Gus parks his car in the lot across from the Space Center, he leaves the driver's window down but locks the car as he walks away.