The first arrival at Andy's house, Amanda, is played by Janet Waldo. Although she had been in films since 1938, it was the gushing teenage character voice of Judy Jetson which led to 40 more years of voice work in animation and video games.
The embroidered front dress that Thelma Lou wears when she has Andy and Helen over for dinner is the exact same dress worn to the Class of '45 Reunion by the character Mrs. Ralph Hanes (actress not credited) earlier this season in Season 3, Episode 19, "Class Reunion."
When Andy, Barney and Opie are in the back room of the courthouse, the "Mayberry Crime Pattern" chart is visible on the wall. This chart was made by Bob Rogers in "Barney's Replacement."
It is at the end of this episode that Andy first declares his intent to court Helen Crump.
This is where it becomes known that Andy's front door has a buzzer, while the back door has a bell. This helps identify which one has the visitor.