The article was printed in the Sunday newspaper's review section while the jury was still considering several outstanding verdicts at the end of the three-month trial.
It was described by Desmond Brown QC, who appeared for the paper at Nottingham Crown Court yesterday after Allitt was sentenced, as a straightforward, unsensational description of Munchhausen's syndrome by proxy - the personality disorder believed to have motivated the nurse to kill and injure.
The article was seen by the paper's night lawyer who took the view that it did not present any serious risk of prejudice. Counsel said it had been a chastening experience for the Observer. Clearly, the system had not worked properly, he said.
Mr Brown said that for the editor, Donald Trelford, who leaves the editorship this weekend after 18 years at the helm, it was a matter of great regret and his apologies were both unqualified and sincere.
But Mr Justice Latham, the trial judge, said he was particularly concerned about the publication because if the jury had seen it, it could have presented very substantial difficulties for the trial. The judge said he intended to refer the article to the Attorney General for him to take a dispassionate view on whether it was appropriate for any legal proceedings to be taken against the newspaper.
Outside court, Mr Trelford refused to make any comment.
Earlier, the judge accepted an apology on behalf of the BBC regional news programme Look North, which screened background material while the jury was still out.
The judge said it was a case where he would have been justified in referring it to the Attorney General, but as the jury had not seen it, no harm had been done and he decided to take no further action.
The Guardian newspaper was also reprimanded by the judge over a leader article it printed after the first two murder verdicts had been delivered but before the jury had finished its work. The judge accepted a written apology from Peter Preston, the Guardian's editor, and said he would not take the matter further.