Hundreds packed into Shrewsbury Music Hall to see the show in which veteran politician Tony Benn headed the line-up.
Benn had ended his half-century career as a Labour MP in 2001 to "devote more time to politics" and concentrate on writing his diaries.
He was joined by Labour MP Barbara Follett, John Redwood for the Conservatives, Liberal Democrat John Thurso and Ned Temko, editor of the Jewish Chronicle.
The TV guide billing for the programme in the Shropshire Star that night actually said that the "panellists include Ann Leslie, John Redwood, John Thurso, and John O'Farrell," so it looks like there must have been a couple of dropouts from the planned line-up and Benn was a late addition.
In any case, in the chair was David Dimbleby. Filming began at 8.30pm and the show went out at 10.35pm.
The questions from the audience were: "Is it appropriate that our Prime Minister (Tony Blair) attend a memorial service for 200 victims of terrorism, and then 24 hours later, meets with a man whose regime is responsible for the deaths of 270 people in Lockerbie?"
The background to this was that Blair had just gone to Libya where he met leader Colonel Gaddafi for a historic meeting in a tent and extended the hand of friendship as Libya, so it seemed, came in from the cold.
Audience question: "Is assassinating a disabled septuagenarian (Sheikh Ahmed Yassin – the spiritual leader of Palestinian group Hamas, killed in an Israeli air strike) a realistic first step to a lasting peace in the Middle East?"
"Should legislation be introduced determining the number of croutons to be served with soup?" The background to this question was that a leading brain surgeon had been suspended after he was accused of taking an extra helping of soup and croutons at a hospital canteen.
"Politicians are trusted by only a quarter of the electorate, so how can they improve their image?"
"What would the panel do to ensure first-time buyers are able to get on the housing ladder?" Among the audience was Shrewsbury councillor Judith Williams, who got a round of applause for suggesting that more should be done to stop buy-to-let housing.
"At this moment in time, where are the panel coming from with regard to the Plain English Campaign's list of our most annoying phrases?"
After the credits had rolled, Tony Benn paid tribute to David Dimbleby in what could have been his last-ever Question Time if he was appointed as the new chairman of the BBC.
He told the presenter, to rapturous applause from the audience, that he deserved to get the post, vacated by Gavyn Davies who resigned following the publication of the Hutton Report. Dimbleby was not appointed – the new chairman was Michael Grade, Lord Grade of Yarmouth – and went on to chair his final edition of Question Time in December 2018, after 25 years, to be succeeded by Fiona Bruce, the first female host of the show.
While in Shrewsbury for that 2004 broadcast Dimbleby paid a warm tribute to the town's cobbled streets and historic buildings when he took a walk around before the start of the show.
He said simply: “I like buildings very much and I like to soak up the atmosphere.”
Sadly we don't have a picture from within the Music Hall that night, but Question Time returned to Shropshire in March 2006, being hosted by Telford International Centre with a panel of Jo-Anne Nadler, Shahid Malik (Labour MP), Sarah Teather (Lib Dem MP), Sir Nicholas Winterton (Tory MP) and author Will Self.
The next Shrewsbury visit came in 2012 when the panel was Baroness Sayeeda Warsi, Stephen Twigg, Caroline Lucas, Germaine Greer and Charles Moore. The venue was the Theatre Severn and there was a small protest outside the theatre before the recording by the Shropshire Fights Back campaign.
Question Time was in Shropshire again in February 2015, this time at Oakengates Theatre. Facing the questions that night were Conservative party chairman Grant Shapps, Labour’s shadow work and pensions secretary Rachel Reeves, Liberal Democrat Tessa Munt, Ukip MP Mark Reckless, and the Sunday Times journalist and critic Camilla Long.
Question Time, which discusses the important local and national issues of the week, was first broadcast in 1979, and is still going strong.