Continuity mistake: People are often shown listening to the radio at completely different times of day to the times shown on the boat.

The Boat That Rocked (2009)
Ending / spoiler
Directed by: Richard Curtis
Starring: Bill Nighy, Philip Seymour Hoffman, Kenneth Branagh, Rhys Ifans, Nick Frost, Michael Hadley
The boat sinks, but they keep broadcasting until the very last minute. The government refuse to come to their aid, but they are promplty rescued by "a boatload of boats" captained by adoring fans who listened to their final moments over the radio. Everyone lives. Everyone is happy. The sixties continue, unabated.
Hazam Thebestone
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Angus: What about this? What about this situation right here? Can't fuck your way out of this one, can you Mark?
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Chosen answer: They can be seen in a couple of long shots of the ship's prow as the DJs shelter there. It's reasonable to assume, given that they were present when the rescue flotilla arrived, that they were picked up as well, just off-screen while the film focused on the main characters.
Tailkinker