Tommy Kirk previously played a Martian in Pajama Party (1964), a spin-off of the Frankie Avalon-Annette Funicello Beach Party series. Yvonne Craig appeared in Ski Party (1965), another branch of that series.
The "Space Center", which looks like a big white mushroom, is not the revolving restaurant at the Houston Airport Marriott at George Bush Intercontinental. While similar in design, the restaurant is far larger. "Space Center" was part of the Collins Radio Antenna Building, 1300 International Parkway, Richardson, Texas, and is now the PCI Health Training Center. The building's two round towers are visible on GoogleEarth.
The Athens Strip was an actual striptease club in Dallas on Greenville Avenue. Bubbles Cash was one of their advertised dancers. Cash used to attend the Dallas Cowboys football games in the Cotton Bowl, and radio announcers covering the game would note that she was attending the game.
Although set in Houston, most of the movie was filmed in Dallas.