The police officer mentions a nearby city as Dixon City. This could be a nod to the "Author" of the Hardy Boys books - Franklin W Dixon.
In the books, the boys aunt was named Aunt Gertrude. It would make sense for her to be called Aunt Trudy in this setting and as she is about 30 years old here.
The watch worn by Joe is Casio Calculator Watch CA53W-1 with miniature keypad for entering the numbers to be calculated. Casio Calculator Watch was very popular during the 1980s.
Towards the end of the episode when Trudy is disciplining the boys in the living room, the tv in the back is a flat screen, which wouldn't have been around during this period of time.