Mark Thompson has been asked to consider disciplinary action
The BBC is to broadcast an apology after admitting a subsidiary company kept £106,000 from premium-rate phone- ins that should have gone to charity.
A further £6,000 will be donated after viewers were accidentally told to ring in to vote in last year's UK Eurovision final when lines were closed.
The errors were discovered during an audit for the BBC Trust.
The money was being kept by call handler Audiocall, which is owned by commercial subsidiary BBC Worldwide.
The BBC said the sums that should have been paid to charity have now been repaid with interest, and that the sum represented only 1.3% of the funds raised for charity via premium-rate phone-ins.
Its director general, Mark Thompson, has been asked by the trust to consider disciplinary action against a small number of staff.
"We would like to apologise to viewers and to the charities for this serious error," the corporation said in a statement.
The BBC raises money for charity through programmes like Children in Need and Sport Relief, on behalf of hundreds of organisations around the UK and the rest of the world.
Scooch won the BBC's Eurovision: Making Your Mind Up 2007 contest
The incidents, detailed in a report commissioned by the BBC Trust, happened between October 2005 and September 2006.
The watchdog's chairman Sir Michael Lyons blamed "unacceptable behaviour from a small number of staff".
He said that a "clear editorial failure" led to the problem with Eurovision, where the phone lines were also being handled by Audiocall.
In the other cases, he said, "the problems were entirely with Audiocall".
Sir Michael added that the BBC Trust was "shocked" to find another problem.
BBC Worldwide sells the corporation's TV shows, DVDs, audiobooks and magazine titles around the globe.
"It is expected to behave to the same ethical standards as the BBC at large," Sir Michael said.
It follows a series of problems for the UK's main broadcasters involving premium-rate phone lines.
On Thursday, ITV was fined a record £5.675m by industry regulator Ofcom for abusing phone-in services in viewer competitions.
SUMMARY OF BBC TRUST REPORT
BBC is "putting right the wrongs" of the past
"Significant" progress by the BBC in putting its house in order
Premium rate telephony service arrangements a "key area" for further work
Past problem discovered with phone votes made when lines closed
Arrangements in place to prevent it recurring
In a separate report released by the trust, the BBC was praised for the action it took after a number of cases involving premium-rate phone lines and other deceptions were uncovered last year.
A new code of conduct for the use of premium rate telephony has been launched and 19,500 staff have finished a "safeguarding trust" course.
New software also stops callers being charged when they phone in outside the time when lines are officially open.
The BBC Trust said: "Overall, and on behalf of licence fee payers whose interest and investment in the BBC we have a duty to represent - we are satisfied that the public can be justified in maintaining its confidence in its BBC."