Architect Doug Roberts (Newman) returns to San Francisco for the dedication of the Glass Tower, which he designed for owner James Duncan (Holden). At 138 stories (1,800 ft/550 m), it is the world's tallest building. Shortly after his arrival, an electrical short starts an undetected fire on the 81st floor while Roberts accuses the building's electrical engineer, Roger Simmons (Chamberlain), of cutting corners. Simmons insists the building is up to standards.
During a routine flight to Minneapolis, a passenger (Susan Dey) aboard Global Airways Flight 502, a Boeing 707, discovers a bomb threat written on the mirror of one of the first-class bathrooms. A second threat is soon found left on a napkin in a galley. Captain Hank O'Hara (Charlton Heston) takes the cryptic threats seriously and follows the instructions -- "Bomb on plane divert to Anchorage Alaska. No Joke, No Tricks. Death"—by changing course for Alaska. To avoid an explosive decompression if a bomb goes off, he flies at lower altitude, increasing fuel consumption.
The film tells the story of Dr. Henry Jekyll (Fredric March), a kind English doctor in Victorian London, who is certain that within each man lurks impulses for both good and evil. One evening, Jekyll attends a party at the home of his fiancée Muriel Carew (Rose Hobart), the daughter of Brigadier General Sir Danvers Carew (Halliwell Hobbes). After the other guests have left, Jekyll informs Sir Danvers that, after speaking to Muriel, he wants Carew's permission to push up their wedding date. Sir Danvers sternly refuses Jekyll's request. Later, while walking home with his colleague, Dr. John Lanyon (Holmes Herbert), Jekyll spots a bar singer, Ivy Pearson (Miriam Hopkins), being attacked by a man outside her boarding house. Jekyll drives the man away and carries Ivy up to her room to attend to her. Ivy begins flirting with Jekyll and feigning injury, but Jekyll fights temptation and leaves with Lanyon.