Glasgow. Two inspectors watch the 'puffer' boat The Maggie coming up the Clyde, remembering the trouble the boat's skipper, Mactaggart caused the last time he appeared. Mactaggart comes ashore, ignoring the concerns of crewman Hamish. 'Wee boy' Dougie stays aboard, and is spotted by two inspectors. Mactaggart is drinking in a nearby pub, railing at Clyde Shipping Services officers, who respond with mocking laughter. When Dougie charges in, he departs with his crew, leaving Dougie to pick up the tab.
The inspectors inform Mactaggart that his license will be suspended unless he carries out £300 of repairs. Gloom descends, until Mactaggart suggests selling a share of the boat, even though it is owned by his sister, Sarah. They visit Mr Campbell at the CSS office; he is too busy to see them, but Mactaggart overhears Mr Pusey, agent to Calvin B. Marshall, head of World International Airlines, talking on the telephone. Pusey is desperate to charter a boat on his employer's behalf, and Mactaggart gladly offers The Maggie.
Mistaking The Maggie for a larger and more modern boat docked alongside, Pusey commissions Mactaggart to carry the cargo of household goods to the island of Killtara, where Marshall has bought a house.
After loading the cargo, The Maggie's crew enjoy a night drinking. The next morning, Mactaggart, ignoring Dougie's warnings, sails out at low tide, and promptly lodges the boat on an underwater tunnel. Mactaggart is forced to wait for the tide to turn, while an amused crowd looks on.
Meanwhile, a horrified Pusey has heard the news, and has informed Marshall, who flies up with Pusey from London. As The Maggie finally gets away, Marshall is visited in his hotel by Campbell, accompanied by Fraser, a journalist who has been having fun with the story, and a furious Sarah Mactaggart.
Marshall and Pusey finally catch up with The Maggie and Marshall orders Mactaggart to return to Ardrishaig with the cargo. Marshall goes, leaving Pusey to oversee Mactaggart. Pusey is horrified to learn that Hamish and Dougie have gone off poaching, and rushes off to find them. Meanwhile, the local Laird has called the police. Pusey finds Dougie, but the Laird spots them and gives chase. Dougie escapes; Pusey inadvertently pushes the Laird in the canal, and is arrested.
Marshall is talking to Fraser when he learns of Pusey's arrest. Pusey's own situation worsens when he discovers that the marshall and the Laird are one and the same.
Marshall charters a plane and tries to track down The Maggie. After trying unsuccessfully to second guess Mactaggart, he finally catches up with him at Inverkerran. He makes plans to transfer his goods to another boat at Oban. But fog forces The Maggie to beach.
Marshall arranges to catch a cattle boat at Loch Mora, and the goods are unloaded onto the decrepit pier. Dougie notices that The Maggie is moored too close to the pier: when the tide comes in, it will catch underneath. As the cattle boat arrives, the pier comes apart, leaving Marshall with no option but to carry on with Mactaggart.
The Maggie stops at Bellabegwinnie, where Marshall argues on the telephone with his wife - who has learned of his 'surprise'. Returning to the boat, he learns that Mactaggart is at a friend's hundredth birthday party. Reluctantly, Marshall attends the party, where he talks to a local girl.
Next morning, The Maggie is still moored. Marshall is furious. He tells Mactaggart he has bought the boat, and will be selling it as junk. In Marshall's cabin, Dougie knocks him unconscious. Meanwhile, the crew learn that Sarah Mactaggart has refused to sell. They head for Killtara. When Marshall comes round, Dougie is unrepentant.
A commotion: the engine has stopped and The Maggie is drifting in shallow waters. Marshall mucks in, and manages to get the engine going, but the boat runs into the rocks. The boat will surely be wrecked, and Mactaggart ruefully prepares to abandon it, until Marshall offers to jettison his cargo, enabling The Maggie to free herself.
At Kiltara, Mactaggart offers Marshall his money back. Marshall accepts but Dougie dissuades him. Later, an unknown puffer, the Calvin B. Marshall, is spotted heading up the Clyde.
