At the end of the episode, Gidget comes to the conclusion that there just aren't major social issues to fight for like when her father was young. But when this aired in 1965, it was the height of the Civil Rights movement including the Watts Riots that took place in Los Angeles (the city the show is set in) in August, 3 months before this episode aired. 1965 was also the beginning of the protests against the Vietnam War which many high school students protested against.
The character Billy Roy Soames is modeled on folksinger extraordinaire Bob Dylan whose signature attire in the 60s was a leather jacket and Levis and who also was given to riding motorcycles.
With soldering gun in hand, Russell is working on an electronic gadget. The tell-tale sign of its obsolescence for those viewing this from a 21st-century perspective is the fact that the gadget works with vacuum tubes, which were still common and viable electronic components in 1965, but were by the mid-1970s replaced by an evolving array of solid-state components, such as transistors and microchips.