Factual errors: C.D. reverses the sequence for getting water to the fire, specifically the hose diameters from the hydrant to the pump, and the pump to the fire
Factual errors: In explaining quarks to C.D., Roxanne (an Astrophysics PhD student who should know better) mentions that there are six types of quarks and that the "top" and "bottom" are the most common kinds. She meant "up" and "down" (which form protons and neutrons). Experimental evidence for the predicted "top" quark was not announced until 1995, 8 years after the film's writing.
Revealing mistakes: As the barn door is open to put out the fire, the "fire bar" (steel bar with gas jets) is visible.
Continuity: When C.D. is sniffing out the fire at the end, he walks to the firehouse, arms down. From the front, his arms are up, from the back, arms down, front arms up, back arms down
Continuity: When C.B. gets a phone call from Chris, you can clearly see that his laptop computer is off. When he comes back to write the letter, his laptop is on.
Continuity: When Charlie is thinking up 20 insults better than 'big nose', he comes up with 25, not 20.
Plot holes: When Chris sees Roxanne for the second time at the restaurant, he goes to the restroom to cool off. He then escapes through the window, unseen. The window he escapes from is only about 8 inches high with a push-out closure that only pushes out about 5 to 6 inches. It is impossible for a grown man with a muscular build to get his body through such a small opening.
Errors made by characters (possibly deliberate errors by the filmmakers): Dixie asks what a light year is and Roxanne describes a binary star. A light year is the distance light travels in a year.
Errors made by characters (possibly deliberate errors by the filmmakers): When Charlie Bales complains about "boring" numbers for astronomical objects, he opposes numbered objects like M31 to named objects like Andromeda. M31 is Andromeda.