Fry mistakes Leonardo da Vinci's name twice as Leonardo DiCaprio, a famous actor who starred in Titanic, which came out in 1997 and Fry mentioned this movie, since he saw it before teleporting to the future in 1999. However, Fry would never get the chance to see movies DiCaprio starred in that were released after 1999 because the Professor told that all films far from the past are extinct.
When in the crypts under Rome, Professor Farnsworth finds the number of steps to walk "encoded" using Roman numerals: "IIXI - (XXIII x LXXXIX)". This is 211 - (23 x 89) = 2048 - 2047 = 1. This is a reference to the fact that 211 - 1 is the first Mersenne number with a prime exponent proven to be non-prime (it has prime factors 23 and 89).
When ship approaches Future-Roma, its name is shown in a similar fashion as the Futurama opening screen.
The roman numerals on St. James' coffin read "IIXI–(XXIII·LXXXIX)". Converted to the decimal system this becomes which equals one. Also, Professor Farnsworth mutters something about the Fibonacci sequence – which contains .