The amusement park featured in this episode is Magic Mountain (now Six Flags Magic Mountain) in Valencia, CA.
Right after the opening titles, Diana's car is "broken down" next to the Korean Friendship Bell in San Pedro, California.
This was filmed prior to Six Flags buying Magic Mountain. Interestingly, at the time of the purchase, the Six Flags Parks were owned by Time-Warner, the parent company of D.C. Comics; the publisher of the Wonder Woman comics. In fact, several Wonder Woman themed rides, including a couple of roller coasters, would start popping up in the Six Flags parks.
Six Flags Magic Mountain was also the filming location for another movie with "phantom" in the title. "Kiss meets the Phantom of the Park" was a made-for-TV movie filmed and released in October 1978, almost a full year before this episode aired.
This 2-part episode marks a reunion for guest stars Jared Martin and Ike Eisenmann. Previously, they both had starring roles on the TV series The Fantastic Journey (1977).