Kick-off at Glasgow’s Hampden Park on the first day of the Games’ sporting action was delayed for about an hour.
The men’s football competition gets under way with eight games later, including Britain v Senegal at Old Trafford at 20:00 BST.
The penultimate day of the torch relay sees the flame visit Buckingham Palace.
The flag mix-up at Hampden Park had been an “embarrassing mistake” and not the start Games organizers would have wanted, but “no great harm was done”.
As the North Korean players were being introduced before the match against Colombia, South Korean flags were mistakenly displayed in the video package.
The squad walked off and could only be persuaded to return when the teams were announced again with each player’s face displayed next to the North Korean flag.
Relations between the two Koreas are tense – they remain technically at war following the 1950-53 Korean conflict, which ended in an armistice.
Speaking after the match, North Korea’s coach Sin Ui Gun said: “Our team was not going to participate unless the problem was solved properly…
“Unfortunately it took some time later for the broadcast to be done again properly and we made the decision to go on with the match.”
It was not immediately clear who had produced the video shown in the stadium.
A statement released by London 2012 organizers said: “We will apologize to the team and the National Olympic Committee and steps will be taken to ensure this does not happen again.”
London 2012 spokesman Andy Mitchell said: “The South Korean flag was shown in the video package on the screen before the kick-off and the North Koreans were naturally very upset about that…
“A genuine mistake was made for which we apologize.”
The opening match in the men’s football gets under way at 12:00 BST at Hampden Park when Honduras take on Morocco, followed by Spain v Japan.
Matches are also taking place at St James’ Park in Newcastle, Cardiff’s Millennium Stadium and the City of Coventry Stadium.
In other Olympics news:
• In the first event of the Games, Britain’s women footballers beat New Zealand 1-0 at the Millennium Stadium in Cardiff. This was one of six women’s football matches played on Wednesday
• Prince Charles and the Duchess of Cornwall visited the torch relay in Tottenham, north London, on Wednesday. On the torch relay’s penultimate outing – day 69, which can be followed live here – the flame will pass through Downing Street and be greeted at Buckingham Palace by Princes William and Harry, and the Duchess of Cambridge
• A global investment conference being held in London on Thursday will kick off a series of business summits intended to showcase the UK and attract investment during
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