Quaid filed the lawsuit in Los Angeles Friday against Deerfield, Ill.-based Baxter Healthcare Corp.
According to the suit, heparin and a lower-dose version of the drug called Hep-Lock are both packaged in similar blue vials with small print on the labels.
Similar medication errors caused infant deaths, and Baxter should have recalled the heparin vials, the lawsuit states.
The Quaid's twins -- Thomas Boone and Zoe Grace -- were born via a surrogate at Cedars in November 2007.
The then 12-day-old babies were given a dose of heparin 1,000 times the normal dose for infants.
A technician had apparently stored the blood thinner in the wrong place, and a nurse grabbed the medicine for the babies without looking at the dosage.
Both babies then started to bleed out and were put in the neo-natal intensive care unit, where they were eventually stabilized.
Quaid and his wife Kimberly Buffington sued the hospital and settled for $500,000 in June 2009.
Cedars also agreed to provide future medical care for the children if they experience problems related to the hospital mishap.
The Food and Drug Administration recalled the drug in March 2008 because of contamination.