Before lunch, South Africa third slip AB de Villiers claimed he'd caught Andrew Strauss on 23 but the England opener stood his ground and replays showed de Villiers had dropped the ball.
Strauss was out soon afterwards, caught behind having added just four more runs, but that didn't stop, according to Arthur, Vaughan from giving de Villiers a piece of his mind at lunchtime.
Then late in the day, Vaughan - diving forward at mid-off - claimed a low catch off the bowling of the recalled Andrew Flintoff which would have seen the in-form Hashim Amla out for nine and reduced the Proteas to 76 for four.
Amla, who scored a century in the drawn first Test at Lord's, was two-thirds of the way back to the pavilion and about to step off the turf, which would have made changing the decision impossible, when 12th man Andre Nel and Arthur gestured to him to stay put.
He did and, belatedly, third umpire Richard Kettleborough was called into play by on-field officials Billy Bowden and Daryl Harper.
With the pictures unclear, Kettleborough had little option but to let Amla continue and at stumps the batsman was 18 not out.
"It's fair to say that AB took a lot of criticism at lunchtime from some of the England players - from Michael Vaughan himself," said Arthur.
"It's amazing there's a lady up there called Mother Cricket, who doesn't sleep - and it came back to haunt Michael Vaughan later in the day.
Arthur explained: "I've always been a coach that has advocated technology. If the ball bounces it's not out. I'm 100 percent sure it bounced.
"It is my business," he said of his move in telling Amla to stand his ground. "Hashim Amla is probably the most polite guy in the world, a very disciplined boy.
"He wouldn't have questioned anything that had happened out there. I felt I was well within my rights to tell one of our key batters, a guy in form, to stay on the ground so the correct decision was made.
"I'd never say Vaughan was dishonest."
He added: "We had two separate incidents, AB thought it had gone from the one hand to the other hand. It clearly hadn't. AB accepted his mistake and apologised straight away out in the middle to Andrew Strauss."
England coach Peter Moores said he had no complaints about Amla's decision.
"I've nothing against Amla, if your team have shouted at you to stay you've got to stay.
"Vaughany caught it clean but when he was in the huddle there was big commotion because of what was on the big screen, it was Vaughany who said to the umpires 'I think you should refer it'.
Moores, who said Vaughan still felt his was a clean catch, said of the de Villiers' incident: "De Villiers has got to decide if he knew (the ball was dropped). I thought it was a disappointing incident."
This series should have been the trial Test campaign for a system, similar to one suggested by former England coach Duncan Fletcher and to one used in professional tennis, which would see the teams allowed to make three 'challenges' an innings to an umpiring decisions.
However, this was vetoed by England with Moores explaining they wanted the umpires to remain in charge of the process.
"We support referrals, we didn't want players doing the referring."
The catching controversies overshadowed a day which saw a much improved bowling performance from South Africa as they dimissed England for just 203 with pacemen Morne Morkel and Dale Steyn taking four wickets apiece.
South Africa closed on 101 for three, a deficit of 102.