When Picard, Data, and Worf sing HMS Pinafore, Picard says "his heart should stamp" during the second verse. Did he misspeak because those aren't the words?
Yes, Picard makes a mistake in the second verse (the lyrics of which we don't see on-screen). The line should be
"His foot should stamp"
but he sings
"His heart should stamp"
Presumably this was due to the stress of trying to fly the shuttle, monitor the mooring clamps and sing, all at the same time.
This seems to just be a production goof (noting that Stewart isn't a particular fan of Gilbert and Sullivan). The script has the correct line.
PICARD: (smiles, triumphant) Prepare the docking clamps.
Worf moves to a rear panel as Picard sings with Data...
PICARD/ DATA'S COM VOICE: "... His foot should stamp..."
As does the film's official novelisation
The captain grinned and in the same soft tone, told Worf- “Prepare the docking clamps.” The Klingon obeyed as Picard sang, triumphant, with his android friend: "Or the tang of a tyrant tongue … His foot should stamp and his throat should growl, His hair should twirl and his face should scowl"