Okubo Toshimichi was a real historical figure who lived from 1830 to 1878. He was killed by a group of disgruntled samurai while he was in a carriage going back to his Tokyo home. The attack did happen on May14th.
The kabuki play near the start of the film tells the tale of "Bakkyusai the Killsword." This name is a pun on "Battousai the Killsword": the "kyu" in the former and the "tou" in the latter (meaning "sword" in the "Battousai" nickname) can phonetically also mean "nine" and "ten." The kanji for "nine" resembles the kanji for "ten," but with a little hook hanging off the right side. Bakkyusai's facial scar resembles Battousai's famous cross-shaped scar, but with a little hook hanging off the right side. Somebody worked really hard to make that joke.
Same location with bridge is used in all three movies for different scenes.
Based on the manga Rurouni kenshin