I always understood that expression to mean that well-intentioned plans or programs often have unintended or unforeseen effects that eventually do more harm than good. It doesn’t relate specifically to sin or damnation or to Catholic moral theology.
For example, the institution of “no fault divorce” in the 60s and 70s was touted as a way to reduce the acrimony involved in the traditional divorce process which relied upon proving that one spouse was guilty of some fault like adultery, abuse, etc. It was supposed to make the divorce process easier on couples who, it was assumed, would have gotten divorced anyway. Well, maybe it did, but it also led to a lot more divorces and a lot less recourse for spouses who wanted to keep their marriages together.
Another example: some years ago the federal government placed a special luxury tax on yachts. The idea was to raise more revenue from people who could afford it. What actually happened, however, was that 1) rich people started buying their yachts outside the U.S. to avoid the tax, and 2) U.S. yacht builders started closing and laying people off. The intention was to raise more money, but the result was little if any new money AND a lot more people out of jobs. So eventually the tax was repealed.
These are the kind of things most people mean when they talk about the road to hell being paved with good intentions.