Act I :

• let the pirate bumper pass - a bumper is a cup or glass filled to the brim, as for a toast
• scuttling a Cunarder - sinking a passenger ship of the Cunard line
• cutting out a White Star - separating a passenger ship of the White Star line from the surrounding ships in order to capture it
• Custom House - a house of office set up to collect levied custom (as at a seaport like Penzance) or exported or imported goods
• the glass is rising very high - weather-glass: a barometer (or possible thermometer), in either case indicating fair weather
• your pirate caravanserai - as "caravanserai" is a sort of inn for caravans and their occupants, the only excuse for applying this word to a group of men it that it rhymes with Chancery (almost)
• References in the Major-General's Song:
  • quote in elegiacs all the crimes of Heliogabalus - even the use of a verse form (elegiacs) could not soften the awful deeds of this most appalling of Roman emperors (212 - 22 A.D.)
  • every detail of Caractacus's uniform - this Welsh king who resisted the Roman invasion of Britain had a somewhat limited uniform in that he painted himself with woad, a sort of blue dye
  • mamelon and ravelin - terms for strategic earthworks: mamelon is a mound used in fortifications, ravelin is a sort of ridge
  • never sat a gee - never rode a horse ("gee" being a childish way of referring to a horse, derived from a word of command to horses)
• Divine Emollient! - something that softens, as poetry apparently does, even for pirates

Act II :

• threatened with emeutes - a French term for riots or brawls
• coster's finished jumping on his mother - costermongers (street vendors of fruit, fish, etc.) were sometimes rather rough characters
• life preserver - a stick or bludgeon loaded with lead, intended for self-defense, but all too often used by evil-doers (as in this case)
• unshriven, unannealed - without having made confession or having received extreme unction