The reason that "Police Story" (the literal translation) had such a plain name was because every time Jackie Chan started a new project in Hong Kong, everyone else followed. For example, when The Legend of Drunken Master (1994) was announced, every filmmaker started making drunken boxing movies. With "Police Story", no one knew what to expect, except a police film, and at that time in Hong Kong cinema, no one had ever made a kung fu police film before.
The mall pole slide also nearly paralyzed Jackie Chan after nearly breaking the seventh and eighth vertebrate in his spine. He also dislocated his pelvis doing it (something hadn't previously known was possible).
The scene where the villains crash through the bus window and fall onto the ground, was an accident. They were really supposed to fall onto the car but due to the air brakes of the bus, there was a pump back, creating space between the bus and the car.
In 1990, Miramax had offered Chan to do a another attempt of the American film market introducing, by introducing which meant acquiring the rights to Police Story 1&2, splice the 2 films into one movie, and proposing to Chan which resulted him to scrapped it.
Between 1994 and 2004, the Hong Kong TV series Police Report adopted the Police Story theme song sung by Jackie Chan, as its own theme. Since 2009, the same song is re-adopted as the theme song of Police Report, but sung by Hacken Lee. Televised job advertisements for the Hong Kong Police also adopted segments of the song.
According to the subtitled trailer, the lyrics for the closing credit song are as follows: "None but my own steely self / and total dedication / I sweat, I bleed / in search of the Great Way. / Lives, put down as wagers, may spin a few sagas / Defying against distresses, so brave / walking around in arrogance, like the lion. / It's onward and march, with consequences known to one's self / Climb and climb, I'll put my name on the clouds. / With pride, I write down the poem of my life / Passion and love, tears and follies - honesty: an end in itself / Life: something to gamble with, when epic stories are retold / Hail the hero with the will of steel who watches the world like a lion / Forward we go / As consequences are known to one's own self / On the double, I must soar over the clouds / Forward I must go... Man must stand sky high."