The BBC failed to pay £106,000 to charity from phone votes in over 20 programmes, including last year's UK Eurovision final, it said.
In the case of Eurovision: Making Your Mind Up 2007, a presenter mistakenly told viewers to vote when phone lines had not yet opened.
The other programmes, which have not been named, relate to Audiocall, part of BBC Worldwide, retaining all money
raised from premium rate calls made by the audience who were mistakenly voting despite lines being closed.
For the first time, the BBC Trust has instructed the Corporation to apologise on air for breach of trust.
It has also asked the director general to consider disciplinary action against a small number of BBC Worldwide staff.
The BBC said the sums that should have been paid to charity have now been repaid with interest. The problems, published in a report commissioned by the BBC, occurred between October 2005 and September last year.
BBC chairman Sir Michael Lyons blamed "unacceptable behaviour from a small number of staff".
He said that while a "clear editorial failure" led to the problem with Eurovision, where the phone lines were also being handled by Audiocall, in the other cases "the problems were entirely with Audiocall".
Sir Michael said the BBC Trust was "shocked to find another problem".
It follows the spate of scandals that have engulfed the BBC and the rest of the broadcasting industry.
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