Called "The ideal visit would see...", it said the Pope could be invited to open an abortion clinic and bless a gay marriage during September's visit.
The Foreign Office stressed the paper, which resulted from a "brainstorm" on the visit, did not reflect its views.
The Bishop of Nottingham said, if anything, it was "appalling manners".
The Rt Rev Malcolm McMahon said: "I think it's a lot worse that we invite someone into our country - a person like the Pope - and then he's treated in this way.
"I think it's appalling manners more than anything else."
The junior civil servant responsible had been put on other duties, the Foreign Office said.
Details of the document emerged after it was obtained by the Sunday Telegraph.
'Song with Queen'
The UK's ambassador to the Vatican, Francis Campbell, has met senior officials of the Holy See to express regret on behalf of the government.
Foreign Secretary David Miliband is said to have been "appalled" by the incident.
Robert Pigott, BBC religious affairs correspondent
It's clear that what the Foreign Office has called "this foolish document" did not reflect government policy. Its tone is clearly frivolous, and it came from junior officials.
But it has, nevertheless, the potential to cause considerable damage. Whether fairly or not, it will leave some Catholics with the impression of a culture within official circles in which their Church's teaching is not taken seriously.
Some will suspect prejudice against faith groups. Perhaps most damaging of all, it could leave an impression that the Pope might be regarded as a figure of fun less than five months before his visit to Britain.
Apart from the pressure on the papal visit from public feeling about sex abuse, and the threat of demonstrations against the Pope, the government needs the Vatican's help in a global diplomatic effort to curb climate change and fight poverty.
How serious and far-reaching the effect of the document is depends partly on how the Church itself responds.
The paper was attached as one of three "background documents" to a memo dated 5 March 2010 inviting officials in Whitehall and Downing Street to attend a meeting to discuss themes for the papal visit.
It suggested Benedict XVI could show his hard line on the sensitive issue of child abuse allegations against Roman Catholic priests by "sacking dodgy bishops" and launching a helpline for abused children.
The document went on to propose the Pope could apologise for the Spanish Armada or sing a song with the Queen for charity.
It listed "positive" public figures who could be made part of the Pope's visit, including former Prime Minister Tony Blair and 2009 Britain's Got Talent runner-up Susan Boyle, and those considered "negative", such as Manchester United striker Wayne Rooney and prominent atheist Richard Dawkins.
The civil servant responsible for sending round the memo said in a cover note: "Please protect; these should not be shared externally. The 'ideal visit' paper in particular was the product of a brainstorm which took into account even the most far-fetched of ideas."
An investigation was launched after some recipients of the memo, said to have been circulated to a restricted list, objected to its tone.
A Foreign Office spokesman said the department was "deeply sorry" for any offence the document had caused.
"This is clearly a foolish document that does not in any way reflect UK government or Foreign Office policy or views. Many of the ideas in the document are clearly ill-judged, naive and disrespectful," he said.
"The text was not cleared or shown to ministers or senior officials before circulation. As soon as senior officials became aware of the document, it was withdrawn from circulation.
"The individual responsible has been transferred to other duties. He has been told orally and in writing that this was a serious error of judgement and has accepted this view."
The Foreign Office said the memo had resulted from discussions by a group of three or four junior staff in a team working on early planning for the papal visit.
A source told the BBC News website the individual since moved to other duties had called the group together for "some blue-skies creative thinking about how to make the visit a success", but their discussions had become "a joke that has gone too far".
The source added that others in the group had been spoken to about the incident, but had not faced any formal action.
I think it's a joke that has gone wrong - light relief that has gone out of control.
Jack Valero, Catholic Voices
Bishop McMahon said he hoped it was meant to be "light hearted".
But he added: "That in itself can be dangerous if these memos move around the departments, they tend to gain momentum."
He said he did not think Catholics would be upset by the memo as they "are used to getting a bad press".
Jack Valero from the organisation Catholic Voices said he was not taking the memo seriously.
"I think it's a joke that has gone wrong - light relief that has gone out of control. And I think Catholics will just take it like this, you know, that they'll think about it today and then they will forget about it."
He said those that have been scarred by abortion would find the joke "a bit thin".
But he added: "In the Catholic church we are used to forgiveness, it's part of our culture to forgive people's mistakes."
Earlier this year the Pope announced 2010 would see the first papal visit to the UK since John Paul II's visit in 1982.
Pope Benedict XVI's visit will take place from 16 to 19 September, during which time he is expected to visit Birmingham, as part of the planned beatification of Cardinal John Newman, and Scotland.
The visit will come in the autumn of what is proving to be a difficult year for the Pope with a wave of allegations that Church authorities in Europe and North and South America failed to deal properly with priests accused of paedophilia.
The Pope himself has been accused of being part of a culture of secrecy and of not taking strong enough steps against paedophiles when he had that responsibility as a cardinal in Rome.
However, his supporters say he has been the most pro-active Pope yet in confronting abuse.