Three of the anecdotes around which David Cameron built his case in the debate became the subject of questioning and raised eyebrows, as reporters, bloggers and Twitter users launched their own factchecking operations.

The £73,000 police Lexus

Cameron claimed that he had visited a police station in Hull where they "had five different police cars, and they were just about to buy a £73,000 Lexus". His accusation drew a sharp response from Tim Hollis, chief constable of Humberside police, who said the Tory leader was wrong on two counts: the Lexus IS-F had been bought over a year ago and hadn't cost £73,000.

"The bulk of our fleet are general patrol vehicles made by Proton which are economic to buy and run," Hollis said. But specialist units needed hi-spec vehicles. "They are driven at speed and the safety of the public and our officers is of paramount importance. The Lexus in question was bought for use by our highly successful roads crime section over a year ago."

The police had paid below the list price, which was in any case £53,000. A Conservative spokesman said: "If Hull police in fact managed to purchase their Lexus for a smaller sum then they are to be congratulated."

The black man from Plymouth

"I was in Plymouth recently and a 40-year-old black man actually made the point to me," Cameron recalled at the debate. "He said: 'I came here when I was six, I served in the Royal Navy for 30 years, I'm incredibly proud of my country, but I am so ashamed that we have had this out of control system with people abusing it so badly.' "

This, Cameron's critics swiftly noted, would have made the anonymous man just 10 years old when he joined the service in 1980.

When Cameron addressed an audience in Plymouth on 8 April at a community college the Plymouth Herald said he was "asked by a man who had emigrated to Britain 45 years ago and had served in the UK armed forces: 'When are we going to look after the British people?' "

Assuming these two unidentified men are one and the same, this would mean Cameron's 10-year-old naval recruit had somehow managed to emigrate to Britain five years before being born. One sardonic comment on Twitter summed up the widespread reaction: "There are no black men in Plymouth," observed Chris Terry. "I live here."

In fact, 2001 census data suggests there may be around 450 people in the Plymouth unitary authority area who describe themselves as black – about 0.19% of the population. None has yet identified themselves as Cameron's interlocutor.

The Crosby killing

Cameron had been in Crosby "the other day", he said, "and I was talking to a woman there who had been burgled by someone who had just left prison and he stole everything in her house and, as he left, he set fire to the sofa and her son died from the fumes and that burglar, that murderer, could be out in four-and-a-half years."

He was referring to the killing, in March 2008, of Ryan Dugdale, 21, by Liam O'Brien. The crime actually took place in Anfield, causing angry calls to the Crosby Herald after the debate from people who felt Cameron was unfairly branding Crosby – part of the new Lib Dem-Tory marginal seat of Sefton Central – as a dangerous place.

"I don't mind anecdotal evidence, but they've got to get their facts right," a local Lib Dem councillor, Jack Colbert, said.