Police in Greater Manchester received 3,205 calls and made 341 arrests during their 24-hour Twitter project.
Every incident was detailed in a series of "tweets", with up to 17,000 people following the force's Twitter feed.
The calls ranged from a rape in the city to human excrement being left on the door handles of a police car.
Chief Constable Peter Fahy said: "We have tried to get a serious message out about the size of officers' workload."
Police said the volume of calls they received in 24 hours from 0500 BST on Thursday was "about average" and reflected a typical day.
Of the 341 people arrested, 126 remain in custody on suspicion of a variety of different offences.
Among the incidents recorded were shots fired in Salford, a child being attacked, a post office being ram-raided, a woman being raped and a car being found burnt out.
Police also received a call from a pet owner who said there was a rat in the house and they believed their cat was responsible.
A woman rang to ask for their help to sue the benefits agency because she had run out of money.
Officers also received reports that a baby was being dangled from the bridge - only for it to turn out to be a dog.
Mr Fahy added: "It's generated huge public and press interest and it has shown how social networking is an excellent way of getting out information out to the public.
"It shows how the types of calls change over the day, as it got later there were more calls about anti-social behaviour and alcohol-related incidents.
"We do get calls that are not directly related to our police work such as calls from people with relationship breakdowns, confused people, or sometimes we have callers who just can't deal with the problems life throws at them."
He said the Twitter feed only reflected a fifth of the force's daily activities.