In 2007, while they were at Cedars-Sinai Medical Centre in Los Angeles, Thomas and Zoe Quaid were accidentally given an overdose of the blood thinner heparin.
Following a speech to the National Press Club in Washington, Dennis said it was the most frightening day of his life, adding: "There were 41 hours where their lives were in the balance."
Dennis, 56, is aiming to raise awareness after discovering medical mistakes like the one that happened to his twins are a widespread problem.
He said: "This is preventable error."
He believes the US health care industry should be more like the airline industry, which he said is "kept on its toes" by the National Transportation Safety Board. The NTSB has helped make flying safer than walking, said Dennis. He said the same thing can happen in health care.
The actor has produced and narrated a documentary about medical mistakes called Chasing Zero: Winning The War On Heathcare Harm, to air on the Discovery Channel in the US on April 24. Dennis said he hoped the documentary will hit viewers in an emotional way.
"If you hit them in the heart, it sets the hands to work," he said.
Meanwhile, two and a-half years after the overdose, Dennis said his twins have "apparently no ill effects" from their ordeal. "We were really lucky to have a happy ending," he said.
Documents became public last June, showing Dennis and his wife had agreed to a 500,000 dollar settlement with the hospital.