Johnson and Sweden's Lotte Neumann, who also scored a 68, finished the day three strokes behind the Australian Karrie Webb who had a magnificent 65.
"We were out there for five and a quarter hours and the pace of play was hideous. Anyone who can't get round in four hours needs shooting," Johnson said.
"If you are a quick player you are penalised and it must drive the spectators mad. They can only see five shots in an hour."
Johnson was out in 32, then dropped her only shot of the day when she drove into a bunker at the 16th. She made amends immediately by holing from 25 feet for her fifth birdie of the day at the next hole.
Webb, the winner in 1995, never looked back after an opening burst of five birdies in her first seven holes to reach the turn in 31. She added two more at the 11th and 12th then had pars to finish with 65.
"I was a little tired over the last few holes. I had a great start and didn't worry about the pace of play," she said after her round.
Many of the fancied players have left themselves with a lot of ground to make up. Annika Sorenstam finished on 72, Laura Davies was on 74 while Alison Nicholas, the US Open champion, had a 75 and Nancy Lopez a 77.Reuse content