Mrs. Hardy is annoyed that her husband Oliver seems to spend more time with his friend Stanley than with her. After a furious argument, Mrs. Hardy says that she will leave him if Ollie goes out with Stan again. Stan suggests that Ollie adopts a baby, which he does. Unfortunately, his wife has left their apartment on returning, and a process server delivers a paper informing Ollie that she is suing him for divorce, naming Stan as co-respondent. The boys are now left to look after the infant on their own.
Needing to replace a light bulb, Stan somehow uses one that blinks on and off with the neon sign outside their window. This causes Hardy to take several nasty falls in the suddenly dark room. Sleepily shoving a baby bottle at the infant, Ollie discovers Stan sucking on the nipple instead and having a wonderful time.
Their First Mistake is a rare film for the duo, as there is no resolution at the end. In the original script, Mrs. Hardy came back to Oliver with adopted baby twins, but so much time and money had been spent on adding Laurel's improvisations that there was no budget left to film it.[citation needed]