Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
The officers decided to have sex in a waiting room at Leratong Hospital while a suspect was receiving medical attention.
Big*, the male correctional services officer from Krugersdorp Prison, and Nina*, a female police officer, were recorded having sex.
In the 15-minute video in Sowetan's possession, Big is seen dancing while waiting for Nina to arrive. He is seen fondling her while she smiles.
SowetanLIVE on Sunday night uploaded yesterday's front page and advised the readers to get the hard copy for the full story.
Sowetan was sold out by midday and the newsdesk was inundated with calls from readers who could not find copies of Sowetan.
Just before lunch time, the full story was uploaded. By late yesterday the articles had received 1,290 comments. It was Tweeted 55 times and had 347 comments.
The Sowetan blog, social networks Twitter and Facebook were abuzz with comments on the story. Sowetan also received calls from police officers who expressed concern about the story and the pictures being published. They, however, said it served Big and Nina right because what they did was wrong.
tebzatbh Twitted: "Well done SOWETAN! Hopefully this will bring back MORALS in people's marriages. Next time people think of cheating on their partners will think twice!"
Lusssh B wrote: "Don't understand why every1 is acting all hectic about that Sowetan article. We as a country have bigger problems".
Other readers said both parties were a "disgrace".
Kgali's said: "That is really immoral and embarrassing for our country."
iAREmatete Tweeted: "The correctional officer in the Sowetan recorded the bonk session and he has 7kids. How irresponsible."
Metro FM presenter Melanie Bala wrote: "Holy cow!! The cover of the Sowetan paper today. Rude!!"
Some felt it was wrong for the pictures to be published.
Another blogger tellingitlikeitis said: "Seriously people ... whoever gave this video to the media destroyed so many lives ... it should have been handled internally..."
yoliswa35: "Sowetan do u have to print such undesirable content in the manner u did 2day - what about kids who read yo newspapers?"
semakalengm said: "I will not tweet about that #Sowetan front cover. its just disturbing especially 4 ppl in uniform!"
Mrs Relo Tweeted: "Tjoooo my Sowetan is sold out ... wonder y??? BBM can't watch face" (sic)
* Not their real names.