Jack claims he had no idea Zoe had to take an IQ test for school and complained about being the last to know, however he did know about it because in a previous episode where Zoe was assigned 100 hours of community service over the course of 13 Saturdays, Jack remarked that it was because Zoe pulled the fire alarm during her IQ test.
Toward the very end Sheriff Carter says he looked up his IQ of 111 and found out that it was average, completely average. Actually on the IQ scale 90-109 is average and 110-119 is considered superior intelligence therefore at 111 Sheriff Carter would be considered to have superior, not average, intelligence. (Zoe's IQ at 157 would place her at the level of Genius where less than 1/4 of 1 percent of the population falls.)
Jo tells Zoë the 75th Ranger regiment motto "Sua Sponte" means "to act without warning." In fact it means "of their own accord."
In the final scene, debris is seen burning up in the atmosphere, creating "shooting stars." Unfortunately, the sky is cloudy and the shooting stars are seen below the clouds. Real meteorites would have burned up long before descending through the clouds.