Character mistake: Once Santino and Ares find John again in the hall of mirrors, John is fighting two of the grunt men that came in with Ares and kills them. Both of which had light assault rifles and weapons on them. John and Ares proceed to empty their pistols out at each other before she runs off with Santino. John then throws his empty pistol away and gets up to pursue his target unarmed and while limping. It is unreasonable to think that someone with his skill and training and experience would not take two seconds to reach down and pick up one of the guns dropped by the two men he just killed before chasing after his target, especially given the highly trained body guard with him accompanying his target. As well as probable encounters with more grunts. To add to this, he was seen doing just this moments before when he had limited ammo and each time he'd down a few enemies he would pick up one of their guns and continue.
Continuity mistake: When John and Cassian see each other through the fountain, they start to shoot at each other when the water comes back up. You hear the civilians around them start to scream and panic, but when the next shot cuts to John shooting through the water, the civilians are walking casually around calmly as if nothing is going on, but then in the next shot they are all running frantically.
Other mistake: After John gets his car back in the second scene, he gets chased by a motorcycle. John opens his car door to knock the biker off - as the bike flips the stunt actor/CGI model totally disappears.
Factual error: The entire NYC subway platform/subway knife fight between John Wick and Cassian appears to have been filmed in the Port Authority Trans-Hudson (PATH) system that goes between NYC and NJ rather than the Mass Transit Authority (MTA) subway system (you can actually see the PATH logo on the exterior of the train cars). The PATH does not go to any of the subway stations announced on the public address system during the knife fight.
Factual error: The party in honour of Gianna, Santino's sister, is held at the Terme di Caracalla (Baths of Caracalla). That site belongs to the city of Rome, and would never be used to host a private party, let alone a party in honour of a major Mob figure. Moreover, the place where John and Gianna meet while she's about to take a bath is the Horti Sallustiani (Gardens of Sallust), which are some 5 km away from the place where the concert is being held.
Continuity mistake: When the motorcycle hits Wick's car during the chase scene at the start, the motorcycle demolishes the front right quarter panel and door, with noticeable pieces hanging off the car. When Wick walks around the car to investigate the driver, the car appears to be in pristine condition.