Here is what I believe to be the correct situation, from over at the Islamic Forum :
"In recent years, controversy flared up due to statements falsely attributed to the great scholar, Shaikh ‘Abdul-‘Aziz ibn ‘Abdullah ibn Baz . He was alleged to have said that the earth is flat, and that one who denies this is a disbeliever in Islam. These unfounded allegations were picked up by Cornell astronomer Carl Sagan , and also reported in The New York Times . Such high profile sources in turn provided fodder to a host of anti-Islamic writers, with which to label Islam as a backward and anti-scientific way of life. There was also much delight amongst followers of various heretical sects, who used these statements to attack Shaikh Ibn Baz – known throughout his life as a tireless defender of Islamic orthodoxy.He didn't believe the world was flat after all. Of course, he did believe the Sun goes round the Earth, and that anyone who says differently is an Unbeliever or Heretic. But he may not have said so authoritatively. Neither did the Catholic Church 350 years ago :
In the letter presented below, Shaikh Ibn Baz affirms his agreement with the position of the classical Islamic scholars on the spherical nature of the earth. He also categorically denies that he said that a person who says the earth is round is a disbeliever.
The letter represents a challenge to all those who have attributed these lies to Shaikh Ibn Baz. Whether they failed to verify sources due to sloppiness, or chose not to due to malice, they are required to retract their statements if they want to salvage any semblance of intellectual integrity.
Text of the Letter
From ‘Abdul-‘Aziz ibn ‘Abdullah ibn Baz to the honoured brother May Allah direct you to what pleases Him. Aamin
Salamun alaykum wa rahmatullah wa barakatuhu…
… As for what the magazine, as-Siyasah has published about me quoting from al-Bayan that was written by the writers of at-Tajamu’ at-Taqadumi in Egypt in regards to me denying the landing of man on the moon and me making takfir [to declare a person a disbeliever] of the one who says it or says that the earth is round or rotates - then it is a pure lie; it has no basis of authenticity. And perhaps the one who quoted it did not intend the lie but failed to verify the quote.
My statement is published and distributed and I explained the response to the one who denies the landing of man on the moon and the kufr [disbelief] of one who says it. Furthermore, I clarified that it is an obligation on the one who does not have knowledge to withhold and not to affirm or deny until some knowledge is attained which necessitate affirmation or denial.
Also, I affirm in the statement what I have quoted from the Allamah Ibn al-Qayyim, may Allah have mercy upon him, that which proves the affirmation of the roundness of the earth.
As far as its rotation, then I have denied it and explained the evidences denying it. However, I did not declare kufr upon the one who upholds it. I only declared kufr upon the one who says that the sun is stationary and does not run on a course because this statement collides with the clarity of the Noble Qur’an and the pure authentic Sunnah which both prove that the sun and the moon both run on a course…
Was-Salamu ‘alaykum wa rahmatullahi wa barakatuhu
General Director of the Offices of General Research, Verdicts, Da’wah, and Guidance
This letter was issued from the office of the noble shaikh with the number: 1/2925 on 7/11/1397.
Also see The Collection and Sayings of Ibn Baz, Vol. 9, where the shaikh makes similar statements in regards to similar lies published in the magazine al-Musawir issue #2166 p.15 of the year 1385 corresponding to 4/15/1996.
 Abu 'Abdullah Shaikh 'Abdul-'Aziz ibn 'Abdullah ibn 'Abdur-Rahman Aal-Baz was born in the city of Riyadh in Dhul-Hijjah 1330 A.H./1909 C.E. He held the position of Grand Mufti of Saudi Arabia, the Presidency of many Islamic committees and councils, the prominent among these being: Senior Scholars Committee of the Kingdom, Permanent Committee for Islamic Research and Fatawa, the Founding Committee of Muslim World League, World Supreme Council for Masjids, Islamic Jurisprudence Assembly Makkah; and the member of the Supreme Council of the Islamic University at al-Madinah, and the Supreme Committee for Islamic Propagation, until he passed away on Thursday 27 Muharram 1420 A.H./May 13 1999 C.E. [Source: http://fatwa-online.com/scholarsbiographie...ury/ibnbaaz.htm]
 Carl Sagan, The Demon-Haunted World: Science As a Candle in the Dark, p. 325
 Youssef M. Ibrahim, “Muslim Edicts take on New Force”, The New York Times, February 12, 1995, A-14
Heliocentricism was never declared a heresy by either ex cathedra pronouncement or an ecumenical council. And as the Pontifical Commission points out, the sentence of 1633 was not irreformable. Galileo's works were eventually removed from the Index and in 1822, at the behest of Pius VII, the Holy Office granted an imprimatur to the work of Canon Settele, in which Copernicanism was presented as a physical fact and no longer as an hypothesis.Another quote from the same source (which BTW is worth reading in toto), about Pope John Paul II's role in re-opening the case:
- Catholic Education - The Galileo Affair
In 1979, he expressed the wish that the Pontifical Academy of Sciences conduct an in-depth study of the celebrated case. A commission of scholars was convened, and they presented their report to the Pope on October 31, 1992. Contrary to reports in The New York Times and other conduits of misinformation about the Church, the Holy See was not on this occasion finally throwing in the towel and admitting that the earth revolves around the sun. That particular debate, so far as the Church was concerned, had been closed since at least 1741 when Benedict XIV bid the Holy Office grant an imprimatur to the first edition of the Complete Works of Galileo.One thing everyone can agree on : The New York Times got it wrong. And in this matter, so did I.