The Identity and Passport Service has failed to enforce overseas travel bans imposed by the courts on nearly 150 convicted drug traffickers.
Mr Reid has said he was merely re-stating guidelines
The service is still trying to trace 15 of the 147 traffickers who have left jail and may have gone abroad.
The government said there had been "no risk to public protection" and that most of those handed bans were in jail.
The Home Office said as it went through reform, "many historic" problems would come to light and be rectified.
Its statement said: "The Home Office and its agencies are going through a programme of wholesale reform. During this process, problems - many of them historic - will continually come to light and will be rectified.
"As the home secretary said last week: 'As we shake the tree, fruit will fall and not all of it will be good fruit.' But identifying and resolving problems is a necessary part of the reform process. We will face up to them and overcome them."
Earlier, a Home Office spokeswoman said during an internal audit the IPS found information shared between it, the courts and the prison service was "incomplete with regard to travel restriction orders (TROs)".
"The issue was rectified as soon as we became aware of it and the passports of all offenders subject to TROs have been stopped," she said.
Guidance will soon be issued to courts, prison governors and the IPS "to ensure that information is accurately and comprehensively shared", she added.
The spokeswoman said the Home Office was still investigating the case of the 147 traffickers, adding that prison governors have been instructed to notify IPS of the releases from prison of those subject to the travel bans.
LATEST HOME OFFICE PRESSURES
26 January....Home Secretary John Reid denies telling judges to give softer sentences to ease prison overcrowding
26 January....England and Wales Youth Justice Board head Rod Morgan quits over youth prisons' overcrowding
25 January....Risk of being a victim of crime in England and Wales rises for the first time since 1995, figures suggest
21 January....Proposals reveal the Home Office may be split in two to cover justice and security
14 January Senior civil servant suspended over failure to update police records of Britons convicted abroad
Shadow Attorney General Dominic Grieve called it "a completely preventable blunder" and compared it to the controversy over prison overcrowding.
"If you're having a problem with the prison population you can argue that you can't always predict how many people are going to be sent to prison," he said.
"But failing in an administrative capacity to prevent people who should have had their passports withdrawn going abroad, is a simple piece of bureaucracy. And I think it highlights how the Home Office has really been destroyed under this government."
Liberal Democrat leader Menzies Campbell said the case added to the Home Office's problems.
"Another day and another disaster - confidence in the Home Office among the public must be at an all time low. Will no one take responsibility for this catalogue of failures?," he said.
On Friday, Home Secretary John Reid was forced deny that he told judges to give criminals softer sentences to ease prison overcrowding.
Although Mr Reid explained he was merely re-stating existing guidelines and serious offenders should still be locked up, two judges released sex offenders, saying they were following his advice.
Mr Reid apologised on Channel 4 News on Friday, saying the government should have realised a tougher stance on crime would lead to a bigger prison population.
"It is a mistake not to forecast that we would require a larger number of prisons than we have got at present, by putting away a greater number of dangerous offenders for a longer period," he said.
"I have attempted to remedy that by a 'buy and build' policy of already asking for 8,000 more prison places."
The Association of Chief Police Officers (Acpo) urged courts not to release dangerous criminals on to the streets.
Acpo president Ken Jones said: "Convicted offenders who pose danger to our communities must continue to be dealt with in line with current sentencing guidelines."
On Friday, Rod Morgan, head of the England and Wales Youth Justice Board, resigned over overcrowding in youth prisons.
Figures released earlier show the prison population in England and Wales is at bursting point, having reached 79,731, an increase of 356 on last Friday.
Conservative MP and former prisons minister Ann Widdecombe told BBC Radio 4's Today programme that Labour had failed to plan properly for rising numbers in jails.
"The rise in the prison population didn't take place last Tuesday afternoon. It's been steadily rising for about 20 years," she said.
"The government simply did not supply the places which the courts require."