I worked in software to help manage this for a while. There are still checklists but they are produced ahead of schedule. Every instrument a nurse takes off the tray is counted and then checked at the end for instance.
Delivery room experience: before stitching my wife, the OB counted the pieces of gauze out loud with the nurse watching. They verbally confirmed the total with each other. A matching count and verbal confirmation were performed after the stitching. It inspired confidence seeing them perform this protocol.
With gauze in particular I think every nurse has a story of "that time we removed the septic gauze" with colorful descriptions of the accompanying smell.
