Cardinal Kasper has a longstanding habit of saying things very confidently on grounds that are not obviously adequate for the confidence, but I think it needs to be pointed out that if the Cardinal is right, doing "much more in prematrimonial catechesis" and using "pastoral work" is simply not going to cut it. The level of failure he is suggesting is so extreme that it could not possibly have come about without extraordinary and culpable negligence on the part of bishops and priests. Bishops and priests exist for the purpose of maintaining and protecting the sacramental order; what Cardinal Kasper is claiming is that they have failed on such a scale that it amounts to an outright betrayal of the laity and could reasonably be said to cry out for serious public penance on the part of bishops and priests who are guilty of letting the situation deteriorate to such an astounding degree.I'm very much in agreement with Brandon's thoughts in the matter.
In any case, as Ed Peters has noted, it is an extraordinarily irresponsible thing to toss out in a public interview as if it were a serious assessment: sacramental validity is not a trivial matter, and if you are going to make a statement like this in public, as opposed to just a private conversation, you had better be doing so on the basis of rigorously established principles and you had better be offering a considerable sight more than vague suggestions about catechesis as your solution.
Too often, it strikes me that Catholic thought on marriage and divorce these days seems a bit like Julia Flyte's in Brideshead Revisited, when on surveying her marriage prospects she considers it terribly unfair that her fellow debutants who are members of the Church of England can marry older sons and not worry about the embarrassments of a "mixed marriage". People seem to see the permanence of Catholic marriage as some sort of an awkward sectarian quirk, which it would be best to find some sort of technical excuse for getting around in most cases.
What this misses is that the Catholic understanding is not simply that marriage is permanent of contracted between two Catholics who are sufficiently devoted to a Catholic notion of marriage. Rather, the Church (following Christ's lead) sees marriage as permanent by nature. That's why if someone wishes to come into the Church and have their current marriage blessed, but was in the past divorced and remarried, the old marriage must be examined to see if it is even possible to bless the current one. The Church assumes that non-Catholics' marriages are permanent by nature too. If the Church holds that non-Catholic marriages are by nature permanent, people need to be cautious about suggesting that most Catholic marriages are invalid because those entering on marriage were insufficiently catechized Catholics. That's only a step away from saying that marriage is not in fact permanent by nature.