When Tom (Bill Bixby) and his son Eddie (Brandon Cruz) spend an evening touring MGM Studios, Eddie just happens to make friends with a curvaceous young lady named Dolly Daley (Victoria Vettri) who has come alone to Hollywood to be a "star." Always on the lookout for matrimonial matches for his dad, Eddie finds out she has no place to stay and invites her to come home with him. When Mrs. Livingston (Miyoshi Umeki) arrives the next morning to find the attractive brunette sleeping in the living room, Tom has a very hard time explaining.

A romantic situation develops after Tom (Bill Bixby) meets Miss Allen (Ann Prentiss), Eddie's (Brandon Cruz) schoolteacher. When Eddie's classmates find out, he's teased and tagged a "teacher's pet." But,when he comes home with a black eye, Tom and Miss Allen decide it's best for everyone if they stop dating. Meanwhile, Eddie has worked out the problem in his own way.

Tom (Bill Bixby) falls in love, and wants to marry a charming model named Lynn (Diana Muldaur) whom he has known for some time. Lynn is also very much in love with him. But when Lynn volunteers to spend a day taking care of Eddie (Brandon Cruz), who is home with a cold, she realizes that she isn't ready for domesticity, or the responsibility of raising a young boy.

Eddie (Brandon Cruz) decides that Mrs. Livingston (Miyoshi Umeki) should have a "someone" of her own to love. So, one day he brings home a five-year-old Japanese boy named Frank (Mitchell Sakamoto) to "give" to the housekeeper. When Frank won't tell his last name, Tom (Bill Bixby) summons a policeman (Bill Dana) and makes a "kidnapping" report. Later, Frank's father, Duke (Pat Morita), and his mother, Kendis (Miko Mayama), appear. But it is a bittersweet reunion. And Eddie concludes that he and Tom can be Mrs. Livingston's "someone."

Photographer Norman Tinker (James Komack) decides to do a story on computer dating and enrolls his boss, Tom Corbett (Bill Bixby), at a computer service to get a personalized report. Very reluctantly, Tom agrees. When Eddie (Brandon Cruz) takes a strong liking to Diane (Sabrina Scharf), Tom's "computer mate," and Diane starts making wedding plans, Tom tells her that he's only doing research for a story. Tears follow.. and then a discussion in which Diane and Tom find out that while you can't fool a computer, you can fool yourself.

When Eddie (Brandon Cruz) balks at leaving for his first day at school, Tom (Bill Bixby) wonders if his child is too young to go. His doubts seem confirmed when the youngster runs away from the classroom and back to the comfort of his home. Returned to school, Eddie gets into a fight and then refuses to go back the following day. A wise word from Mrs. Livingston (Miyoshi Umeki) and a little reverse psychology on Tom's part solve the problem. But not without a touch of painful "growing up" for Eddie--and his father.