I have a sad confession to make: I used to love BBC’s Question Time so much that I would only go out on a Thursday night if it meant coming home in time to watch it live. Now it just makes me sad. With public discourse increasingly polarised, all views cheered or jeered by a baying crowd online and off, Question Time is the public square where we get to watch bears being poked. It not only televises the deep divisions in the country, but the uncomfortable position the BBC adopts to straddle them.

Since replacing the veteran broadcaster David Dimbleby with Fiona Bruce, the show has stirred up a hornets’ nest of right/left division in just three episodes, ending last week with a clarification about whether Labour or the Tories were ahead in opinion polls, which reminded us why BBC bureaucracy is the subject of such satire.

To recap: Bruce’s second episode prompted loud support from Conservative voices such as Sarah Vine and the Telegraph but more than 100 complaints over the show’s treatment of the shadow home secretary, Diane Abbott, and a Momentum petition for an apology.

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By replacing Dimbleby with a BBC newsreader best known for helping members of the public sell things they find in the attic on Antiques Roadshow, the BBC hoped to find a figurehead who spoke for the ordinary viewer. She is more shire than Westminster; no wonder the Telegraph, which sends Bruce to report on nice holidays, loves her.

The affair raises important issues for the BBC about impartiality and trust. Ofcom, currently reviewing its news division, said when it was launched: “As national debates become more polarised, it becomes harder for broadcasters to be seen to be accurate and impartial. The BBC has to ensure it devotes the appropriate resources to maintain its position.”

Here are some suggestions. First, spend time and money on basic fact-checking. The presenter of Question Time does not need to have an encyclopaedic knowledge of Hansard, but a proper knowledge of that day’s opinion polls is pretty much baseline. When a politician claims their party is “level-pegging” in the polls, the presenter cannot sneer, as Bruce did, “you’re behind, Diane” without knowing for sure they are right. Again, this is not just a criticism of Bruce. Why was there no producer whispering in her ear “actually Fiona, the polls are little more complicated than that.”

Play Video 0:43 Question Time: Fiona Bruce misstates Labour's position in the polls - video

Everyone makes mistakes, even the best, most knowledgeable journalists muck it up, especially when live on air and dealing with tricky politicians and panellists. Why can’t the BBC simply admit an error quickly and with grace and move on? Instead, its often weird approach makes things worse.

Having failed to offer clarification by the end of the Abbott show, the BBC instead issued a weird statement 24 hours later mentioning “inaccurate and misleading” social media comments. Then on Twitter it stated: “A YouGov poll published on the day of the programme suggested a lead for the Conservatives. Diane Abbott was also right that some other polls suggested Labour either as ahead or tied, and we should have made that clear.”

Then, Bruce waited until halfway through the next show to issue another clarification of sorts. “I just want to pick up on something from last week’s programme,” she began. “There was some discussion about opinion polls … I was talking about a poll which came out on the day of the programme which suggested the Conservatives were ahead. The shadow home secretary mentioned some other, earlier polls which showed Labour in the lead and we should have made that context clear, and I’m really happy to do that now.”

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The timing was to “fit in” with the flow of the show, but the tone was a bit “you ordinary people out there probably don’t even care about the polls.” Which may be true, but everyone who pays for it cares about the BBC getting it right and not being too grand to admit when it gets stuff wrong. It simply needs to be transparent rather than defensive when it makes mistakes, which are tiny in comparison with its vast output but nonetheless magnified not just by its vexatious critics but its own flat-footed reactions.

The increasingly fractious treatment of people in the public eye is enough to make anyone defensive, of course. BBC journalists talk privately of being so hounded after admitting minor errors they vow never to do it again unless forced.

Finally – and this is more difficult for a broadcaster keen to generate debate and maintain audience figures – Question Time needs to stop being so confrontational. The editor, Hilary O’Neill, promised “adrenaline-packed Thursday nights” when she was appointed. Yet 18 months later few seem concerned that the hormone not only sets pulses racing but closes the ability to think clearly.

Ever since the appearance of the far-right leader Nick Griffin in 2009 gave the show its highest-ever ratings of 8 million, the show has increasingly courted controversial guests. Hence, Nigel Farage appears more frequently than his position would perhaps warrant.

Seek out controversy by all means but realise that the end result is a dead bear, not valid debate.

Of all the issues facing the BBC, the calm marshalling of facts is the most important, mostly because it is the central weapon against allegations of false equivalence. On climate change, the BBC no longer insists on seeking out the one voice who rejects the consensus. Impartiality does not mean saying that both sides are the same, when facts suggest that they are not. Fear of abuse does not help here either.

One example from Question Time in recent weeks that has prompted fewer headlines concerns a comment Bruce made about the referendum campaigns. When an audience member said leave ran a “dirty campaign”, Bruce responded that there had been “questions over both leave and remain”.

Paul Lashmar, the investigative journalist behind the documentary Who Paid for Brexit?, complained to the BBC that remain’s use of occasionally inaccurate economic forecasts was not the same as being fined and investigated by the National Crime Agency. There has been no response yet.

These are difficult issues and, in the hurly-burly of a political debate, no one will always get it right. Bruce made a great start in her first week acting on behalf of the audience. The presenter of Question Time needs to speak for the audience, not play to it; a journalist, not a celebrity.

Ofcom’s own research suggests that the BBC gets it right most of the time, with high scores for trust and accuracy. The BBC could argue that the “ordinary people” who watch the show, rather than sad journalists who like to comment, don’t care about political spats and Twitter apoplexy. But those pesky opinion polls show that they do care about the BBC, as should we all.