Factual error: With the radiation belt on fire, the icecaps begin to melt. The Seaview is bombarded by huge chucks of ice. The ice is sinking to the bottom like stones. Ice floats, it doesn't sink.
Factual error: The "Colours" were not flown whilst the Seaview was docked in New York harbour.
Factual error: After leaving the New York conference and hurriedly returning to the Seaview, they didn't ask permission to come aboard.
Factual error: When the sub is being pelted by huge chunks of ice (which should float, not sink, as mentioned earlier), the sub is not knocked off course or damaged in any way. (00:20:00)
Answer: Admiral Nelson is puffing on cigars in a few scenes, and his cigars are even a source of dialogue in the film. Specifically, when his quarters catch on fire, the blaze is initially blamed on a lit cigar, to which Nelson angrily replies that he ran out of cigars before the fire ever occurred. So it's a pretty good bet that Nelson was carrying a cigar (or cigars) in his shirt pocket.
Charles Austin Miller