First, as to the gradation of sin:
The Catholic Church recognizes that some sins are "worse" than others. For instance, it divides sins into mortal sins and venial sins (CCC 1854-1855):
1855: Mortal sin destroys charity in the heart of man by a grave violation of God's law; it turns man away from God, who is his ultimate end and his beatitude, by preferring an inferior good to him.
Venial sin allows charity to subsist, even though it offends and wounds it.
As for this division between really bad sins, and less bad sins, The Church cites the distinction already evident in Scripture (1 Jn 16-17):
If any one sees his brother committing what is not a mortal sin, he will ask, and God will give him life for those whose sin is not mortal. There is sin which is mortal; I do not say that one is to pray for that. All wrongdoing is sin, but there is sin which is not mortal.
Furthermore, even within the "mortal sins", The Church makes further distinctions in regards to gravity: " The gravity of sins is more or less great: murder is graver than theft" (CCC 1858).
What makes a sin mortal? The general rule stated above is that a mortal sin is one which destroys charity in the heart of man by a grave violation of God's law, turning his heart away from God. The Church has tried to further clarify the characteristics which make a sin mortal (CCC 1857):
For a sin to be mortal, three conditions must together be met: "Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent."
a) Grave matter is specified by the Ten Commandments (CCC 1858).
b) Mortal sin requires full knowledge and complete consent (CCC 1859). The older term "material sin" was used in circumstances where one of these two were lacking.
Has the seriousness of sin changed?
Objectively speaking, the seriousness of sin has not changed. To kill a man is just as objectively evil as has ever been (for instance).
However, the guilt assigned to the sinner for his sins may indeed change from time to time, or be different from culture to culture; this has to do with "full knowledge" and "complete consent".
Imagine a society where watching pornography is fairly common. Those born into this society, and who are not taught otherwise, might come to believe that watching pornography is not a sin --- or if a sin, a very minor one, like being impolite to your parents. Such a person would clearly get the facts wrong. But it may really be possible for such a person to come to be ignorant about the gravity of this offense. The Church teaches that in such cases the guilt may be diminished (CCC 1860):
Unintentional ignorance can diminish or even remove the imputability of a grave offense. But no one is deemed to be ignorant of the principles of the moral law, which are written in the conscience of every man. The promptings of feelings and passions can also diminish the voluntary and free character of the offense, as can external pressures or pathological disorders. Sin committed through malice, by deliberate choice of evil, is the gravest.
But supposing that, on the contrary, there were civil laws that made it rather difficult to obtain access to pornographic materials. Then a person couldn't claim ignorance (or at least couldn't claim full ignorance): for in trying to violate the norm he would most likely inquire as to the reason for the ban in law of the prohibited action, or at least be nebulously aware that the act in question is seen as wrong in some way, and that would awaken his conscience into action (if this person be morally mature at least to some extent). And in any case, it could not be said that such a person acted without "deliberate intent". But if there was free intent, then there was consent.
On the other hand, in a society which doesn't prohibit access to pornography and/or makes it readily available as an acceptable choice, the conscience of him who wishes to access pornography and who has never been taught that access to pornography is wrong might not be awakened nor disturbed to the sin he is attempting. Nor might his conscience/reason/mind give him the opportunity to deliberate as to what he is attempting is wrong, or whether he consents to it: for instance, he might access pornography to an extent because his friends are doing it and not based on a careful analysis of his actions.
Thus, given the circumstances of time, place, culture, education, upbringing, cultural influences, our own psychological make-up, and sometimes our own passions, etc. the guilt imputed to the sinner for a particular sin may indeed be diminished. Notice, however, that THIS IS NOT A GOOD RESULT. The objective evil of the sin remains just as bad! The fact that people and societies do not perceive the full nature of their actions is not a sign of health, but of decay. It is the action of The Evil One leading people astray. And the fact that God doesn't punish these sins as badly as they deserve has nothing to do with the how holy (or how sanctified) the particular person who commits them is --- on the contrary, it has everything to do with His Mercy and how spiritually sick the sinner is.
"A World Without Sin" (Assuming one believes all the foregoing).
One particular (evil) route towards people being free of the guilt of sin might go as follows: Corrupt society and its education so much that all individuals lose any inkling as to good and evil; then any and all of their actions will be entirely devoid of any considerations or knowledge about the divine law; and thus, the argument goes, they will be entirely free of any guilt due to sin.
This will not work, because:
a) As The Church teaches (CCC 1860), the moral law is written deeply into the hearts of men, and as such it is not easily eradicated. The promptings of our conscience in regards to the moral law will always be there, even if severely muffled by the culture around us. Certainly men can be taught to ignore these promptings, much like they can be taught to ignore (certain amount of) pain, but it is not a given that all men will ignore their consciences forever, and those who don't will inevitably speak up (if given an opportunity). Yes, these men can be silenced as good men are always silenced in despotic regimes, but this silencing will have to be continuous throughout the existence of this culture.
b) Even if such cultural programme can be carried out, I don't think that the society which puts it into effect will survive in the long term. After all, disobedience to the entirety of the moral law cannot lead to a flourishing society, but rather to unmitigated chaos. In a society where anyone can lie in open court about the action of his neighbor, where anyone can feel free to hunt his neighbor (before kidnapping his neighbor's wife for himself), or where no authority higher than oneself is recognized --- such a society cannot last for very long.
c) As The Church teaches (CCC 1860), the "full knowledge" clause applies to unintentional ignorance. If one intentionally makes oneself ignorant of the implications of the moral law, or if one intentionally forgoes educating oneself in these implications in order to avoid the responsibilities therefrom (as the proposal suggests), one doesn't avoid the guilt and/or penalties of sin.
c) Finally, let's look at the original assumption behind the suggestion. The assumption behind the proposal is to avoid guilt/punishment for the sins committed and not necessarily to come closer to God and grow in holiness. Clearly this is not a very mature motivation for a Christian! To forgo flourishing in order to gain the pity of God in regards to our sins is analogous to the idiot who intentionally makes himself blind in order to obtain the societal benefits that are given the blind because they are at a disadvantage.
There is nothing I know that says that sins "lose their potency" as times goes by, or as societies become more "evolved" or "enlightened". A sin remains as evil as ever objectively speaking.
Now, there can certainly be an appearance that some sins are less wrong today than they used to be --- and this is nothing but an optical illusion --- because (I think):
a) They are more common in our society today than they used to be --- The Evil One has certainly been making advances of late in some areas ---, and
b) People have an intuitive notion that their sin is less grave because it is now more common. People who think so are intuitively picking up on the fact that under the new circumstances they can have less knowledge about the nature of their actions and they can have less deliberate intent to commit them. But they are wrong in thinking that their now common sin is less grave. It remains as grave as ever --- it remains as evil as ever. What they are intuitively trying to grasp is that they are imputed less guilt now for their evil deed than they had been in the past because now they have some mitigating circumstances. In other words, people confuse the gravity of the sin with the amount of responsibility they have for it. Their responsibility for the sin may be diminished, and therefore they conclude that the gravity of the sin has diminished --- But this is incorrect. The evil of an action and the harshness of the punishment for it are different things.