In the episode "A New Doctor in Town" a shot of Dr. Petersen driving away from Floyd's shows the old Mayberry movie theater being renovated for some other production. By this episode, as Andy drives by the old theater, it has now become a paint and wallpaper store.
When Helen finds out that the lawyer, 'Lee Drake,' that Andy visited in Raleigh was a woman, she gets jealous. In an attempt to mislead Helen, Andy describes the pretty lawyer as 40ish, heavy-set, and grim. In reality, the actress who played 'Lee Drake' (Whitney Blake, who also played 'Dorothy Baxter' in the sitcom "Hazel"), was 41 years old when she appeared in this episode, so she actually WAS in her 40s (although she certainly wasn't grim). For the record, she was the same age as Andy Griffith, but was seven years older than Helen (Aneta Corsaut).
Andy says it's over 100 miles from Mayberry to Raleigh. It is in fact close to 140 miles distance (based on Mount Airy), which would involve a little over two hours to drive.
When Andy assures Helen that Howard will have her dancing every second she sarcastically replies "Zowey!" This was a catchphrase made famous by comedian Joe E. Brown.
When Andy returns to Mayberry from Raleigh, and pulls up in front of Emmett's Fix-it Shop (parking on the wrong side of the street), we can see that Aunt Bee's car has Curb Feelers on it.