Other mistake: When the train stops Godfrey gets off to relieve himself but when he is climbing back in to the carriage the train appears to be already moving at speed because the background projection started moving too early.
Andy and Helen Get Married - S1-E1
Other mistake: Sam Jones' son, Mike, tells Aunt Bee that the farmhouse has been in their family for 150 years. While showing Aunt Bee a photo album, he points to a photo and says, "That's my great-great-grandfather who started this farm." Pointing to a woman in the same photo, Mike says, "That's my great-grandmother. She lives in Philadelphia." It is very unlikely that the daughter of a man who had started a farm 150 years earlier would still be alive. Assuming the man started the farm when he was in his 20s, he would have had to father a child when he was in his 70s and she would now have to be in her 100s.
Other mistake: The CSI technician dusting for fingerprints on the gun isn't wearing gloves. He proceeds to pick up the gun in his, ungloved hands and hand it to an ungloved police officer thereby adding their fingerprints to the gun. Very sloppy police work.
Log 51: A Jumper, Code 2 - S1-E19
Other mistake: Halfway through the show, the officers walk across the street to talk to some young toughs. The school sign painted on the street is spelled "Schol".