Saying about terrible police responses, Zhao Xiaodong comes to mind.
He had already killed some people before the bus siege, but the bus siege is the main part of the disastrous response from police:
At 1 p.m. Zhao boarded a bus at Podi (坡底村), a village one kilometre north of the bridge, and a quarter hour later it approached the structure from the northern end, where it was stopped by police for inspection. The county cadre soon spotted Zhao and in panic rushed out of the vehicle, yelling that he was on the bus, whereupon Zhao drew his pistol, shouting: "Quick, drive! Drive!", at the same time firing a shot at a police officer, injuring him. The bus driver tried to use the gunman's distraction to escape, however, Zhao noticed this, shot him as well, and afterwards threatened the other passengers that he would kill anyone who dared to move. He then put himself behind the steering wheel and drove towards the bridge, while one of the guards outside opened fire with a Type-56 assault rifle, hitting him in the cheek and penetrating several of the bus's tires. 600 metres down the road Zhao finally lost control over the vehicle and crashed into the bridge railing, leaving it stuck, with the right front wheel hanging off the bridge.
Soon the bus was surrounded by members of the police and armed police, with a squadron approaching it, sheltered behind a postal car. Halting 30 metres from the bus they ordered Zhao to drop his gun, however, he opened fire and threw a bomb at them, causing hand injuries to one of the officers. In the ensuing gunfight with police, Zhao was seriously injured, but still continued to shoot at his besiegers, while several of the passengers tried to seize the opportunity to escape. Zhao noticed this, shot several rounds at them, forcing them to take cover behind their seats, and then resumed firing at police, injuring the squadron leader in the process. Witnessing the wounding of their leader and hearing Zhao shooting the passengers, the armed police forces indiscriminately opened fire at the bus and continued to shoot, until they were hastily ordered to stop by their team leader and instructor. Shortly after the shooting stopped a male passenger jumped out of one of the bus windows.
At approximately 1:40 p.m. the director of the Jili branch office, the city police captain, and others arrived at the scene, ordered to cease all shooting, and to get a fire truck and a truck loaded with cement bags. At 2:20 p.m. members of the armed police eventually used the cement truck as cover to approach the bus, while the fire truck sprayed it with foam, to impair Zhao's view. Zhao continued to shoot at both vehicles, while the armed police returned fire. During the gunfight a second passenger managed to escape. Ten minutes later, when the police officers saw no more movement inside the bus, they stormed the vehicle through the rear window and discovered Zhao's body, who had been hit by sixteen bullets. By the time of his death he had only three rounds of ammunition left. The surviving passengers were rescued and at 2:40 p.m. the siege was finally declared over.
Overall 68 members of the police and armed police participated in the siege, during which one police officer and two members of the armed police were wounded. In total they fired 528 rounds at the bus, leaving all of its windows broken and 375 bullet holes in the vehicle's body. Of the 17 people who were originally in the bus beside Zhao, Zhao killed five and wounded three, while seven others were killed by bullets fired by police and armed police, and the two remaining escaped by jumping out of the vehicle. Additionally, ten other people were accidentially injured during various stages of the siege.
Source: Amok Wiki's article on Zhao Xiaodong