This is Jackie Chan's favorite of his many movies, and it always turns up on lists of the greatest Jackie movies ... hell, the greatest HK action movies of all time. It is among my favorites, as well, although when I made my Top 50 list some years ago, it was Supercop (Police Story 3) that made the list. I also have a soft spot in my heart for Armour of God 2: Operation Condor, which is admittedly inconsistent and even occasionally awful, but which finishes with a colossal wind tunnel scene.
Police Story features two of Chan's best set pieces, a battle in a town that starts the film, and arguably his greatest scene, an extensive fight in a mall. There is enough between those two iconic scenes to keep your interest, but no more than that ... as great as Chan is (and he is one of the true GOATs), I don't know if he's ever made a perfect movie (his comedy works great in the action scenes, when he truly is the Buster Keaton of his day, but it is less effective outside of those scenes). There was an odd video store back in the day in Berkeley ... this was before DVDs, so everything was VHS, the owner was a wonderful snaggle-toothed guy, and every morning they put a life size replica of Robot Monster outside the front door ... they had this one tape that was nothing but 8 hours of Jackie Chan stunts.
On the plus side, Police Story features Brigitte Lin, who is not only supremely talented but who was, in the years when I watched a couple of HK films a week, my choice for most beautiful Hong Kong actor (her, or Tony Leung). On the minus side, it also has Maggie Cheung, whose character (Jackie's girlfriend) also turns up in the next two sequels. Cheung is usually marvelous ... she co-stars with Leung in In the Mood for Love, which still gets my vote as the best film of the 21st century ... but her character in the Police Story movies is a pain in the ass, unworthy of her (in fairness, in 1985 she was barely 21 and had been in only a few movies).
Still, if you start with a great action sequence, and you end with an even greater action sequence, you can forgive a lot of the rest.
Here is the mall scene. At the end, when Jackie slides down the pole, the lights were hot, resulting in second-degree burns for Chan (he also dislocated his back and injured his pelvis). Note that Brigitte Lin did some of her own stunts. And you can see why the stunt crew referred to this film as "Glass Story".
Here is Chan talking about the final stunt: