Come the late 60s, a smoother, more comfortable plastic would be used for the outer layer of the diaper, and adhesive tapes were added to remove the need for rather dangerous safety pins, along with allowing for more secure fastening for a better fit, and Pampers would also introduce a quilted layer above their padding, trapping liquids under it and reducing moisture from a baby's bottom after wetting to prevent discomfort.

Although with tapes came a slight design flaw, while more secure than pins, once the tapes are placed, there's no refastening them for a better fit. And if you even try, you'll end up ripping the diaper's surface and ruin the tape at the same time! Not to mention these diapers were still significantly lacking when in came to preventing leaks, as their prefolded design still suffered from leaking out the sides from an overall poor fit.

Perhaps just absorbency wasn't enough, and maybe the shape of a diaper played a role in its effectiveness, and in the late 70s, a new type of diaper would be introduced that would change the industry forever...

If you would like to know more about diapers during the 1970s,  marshallfox.1971 has this great post about Kimberly-Clark's first diaper design; "Kimbies" you can check out:
https://www.furaffinity.net/view/18253648/