Billy's line "Just call him 'The Scottish Chef'" is a sly reference to the superstition in the theatre that it is bad luck to mention the title "Macbeth" - instead it is usually referred to euphemistically as "The Scottish Play".
The line spoken by Harry Gibby, the health inspector - "...the sins of a bloke what has made me work for my pound of flesh..." - is a reference to another play by William Shakespeare, 'The Merchant of Venice'.
'Pigs will fly' is sung by the bin men to the tune of 'Colonel Bogey'.
Gordon Ramsay is a well-known and successful British chef and restaurateur, and has made many television programs about restaurants and cooking.