A glitch that cut off the last moments of David Letterman’s last show in parts of Canada may prove costly for the country’s television industry, as its regulator investigates the incident.

Fans across Canada complained to the Canadian Radio-television and Telecommunications Commission about missing David Letterman’s May 20 goodbye speech, a performance by the Foo Fighters, and a photo montage of Mr. Letterman’s career. Cable subscribers say they were switched over to another program before the final Late Show could end. One...