Crew or equipment visible
Errors in geography
In a frigate that has 'beat to quarters' and is 'cleared for action', the Captain's cabin would be opened up to the rest of the ship and gun crews would be manning the guns in the cabin. There would be no way Aubry and Maturin could have remained there.
Incorrectly regarded as goofs
However, utilizing the codes, it seems they possibly signal starting at the mizzenmast: "Telegraphic Signal (red/white diagonal) then send "392" ended with a "substitute" flag. Possibly standing for "impossible-ility" the flags on the mainmast seems to indicate "602" or "part-ed-ing-ition" without a "Finished" flag as per the 1803 and 1806 code books referenced above. This doesn't seem to mean much of anything and may have been the crew hanging random flags.
As an aside, Popham's Signals were famously utilized by Nelson at the Battle of Trafalgar when he signaled: "England expects that every man will do his duty."
Though never stated in the movie, in the book Far Side of the World, Pullings has been promoted to Master and Commander (though not given command of a ship) and is along as First Lieutenant as a volunteer. Captain Aubrey refers to him often as 'Captain Pullings', the courtesy due a Master and Commander.