Broadcast watchdog Ofcom are still investigating the Newsnight programme.
After the BBC Trust released their findings a spokesman said:
Ofcom's investigation into the Newsnight child sex abuse allegations is currently ongoing.
We will make the outcome of this investigation known in due course.
The BBC Trust also found that the Newsnight failures came in the immediate wake of the decision not to run an investigation in to Jimmy Savile and said that the situation had led to a "lack of clarity concerning who had overall editorial responsibility for the content of the Newsnight report".
They said: "Concern about possible reputational damage in that event 'played too large a part' in the decision to proceed with the broadcast."
"The Trustees were clear that there was a failure of editorial control within the BBC; this was a high-risk report which required rigorous supervision and did not receive it."
The BBC Trust found that, although Lord McAlpine denied the allegations when he was contacted by a Channel 4 News journalist before Newsnight was broadcast, the BBC still made no attempt to contact the peer, which it should have done.
Trustees also said that concerns had been raised previously about the credibility of some of Mr Messham's evidence - which was known to members of BBC Wales, but no effort was made to contact them.
The Trustees considered that parts of BBC News not contacting colleagues in the nations and regions when investigating stories on their patch was very poor practice.
The report from the BBC Trust's Editorial and Standards Committee said the failure by Newsnight was "extremely concerning".
It found that the freelance reporter Angus Stickler, who brought the story to Newsnight, was considered a "safe pair of hands" and may have been subjected to "lighter-touch editorial checks" than if he had been less well-known to the BBC.
It said the report was wrongly treated as if it had two sources, Steve Messham, and an interview with a second victim broadcast on BBC Five Live in 2000, who could not be contacted during the making of Newsnight.
– BBC Trust's Editorial and Standards Committee
The Trustees agreed that members of the Newsnight team were wrong to regard this as a report with two sources, given that the second witness could not be found.
The Trustees found it particularly concerning that, at no point in advance of the broadcast of the Newsnight report, was Mr Messham shown a photograph of Lord McAlpine and asked to confirm that he was the individual at the centre of the allegations.
The BBC Trust has said that the airing of a Newsnight report which led to Lord McAlpine being wrongly named as a paedophile resulted largely from a failure by members of the team to follow the BBC's own editorial guidelines.
The broadcast on 2nd November was a "grave breach which had been costly to all concerned" and resulted in the public being misled, the Trust's Editorial Standards Committee (ESC) found
And in its findings, the committee ordered another report by the BBC next year into what steps will be taken to make sure the corporation "learns from these events".