And those aspects are considered heretical. Anything that goes against a Catholic dogma is heresy by according to the Catholic Church; so if it "disagrees" with it, it means it's heretical.
Now, the term "heresy" and "heretical" tend to be used a lot less nowadays, and more applied to what would be regarded as the
major heresies to emphasize their, well, majorness. Certainly, Calvinism (according to Catholicism) would be considered more correct than something like Unitarianism. Thus in the interest of terminology, actually using the term heresy may be improper due to its connotations. Still, I feel you're attempting to make an artificial distinction here between "disagrees with" and "heresy."
It is true that double predestination is condemned by the Catholic Church, as seen in the sixth session of the Council of Trent:
Canon VI. If any one shall say, that it is not in the power of man to make his ways evil, but that God worketh the works that are evil as well as those that are good, not by permission only, but properly, and of Himself in such wise that the treason of Judas be no less His own proper work than the calling of Paul; let him be anathema.
However, I should note that not all Calvinists accept double predestination. Actually, I'm not even sure if most of them do.
This is another case of something that some Calvinists believe in but some don't. Or more specifically, the interpretation of what "Limited Atonement" is. Here is an analysis of the Five Points of Calvinism (Total Depravity, Unconditional Election, Limited Atonement, Irresistible Grace, and Perseverance of the Saints) by a Calvinist-turned-Catholic:
As a Catholic who is a former Calvinist, I am very interested in the relationship between various Calvinist doctrines and the Catholic faith...
freethoughtforchrist.blogspot.com
They assert that, except for Perseverance of the Saints, a
sound Calvinist interpretation of those points (they repeatedly differentiate between "sound" Calvinist interpretations and "unsound" Calvinist interpretations) is completely in line with Catholicism. This includes Limited Atonement. I won't quote the entire thing they wrote on this, but the quick summary quote is:
In the words of the Council of Trent (Sixth Session, Chapter III--page number removed), "though He died for all, yet do not all receive the benefit of His death, but those only unto whom the merit of His passion is communicated." This is all that Calvinists typically mean by "limited atonement." Christ died for all men, in that his atonement is sufficient to save all men, in that it provides sufficient opportunity and grace to enable all men to be saved if they will choose to avail themselves of their opportunity, and in that God intended it to provide such objective opportunity to all men and to make possible the free and sincere offer of the gospel to all men; though, in his eternal plan, he predestined that the atonement would only actually end up bringing about the eternal salvation of the elect through the application of divine grace. All this both Catholics and the sounder Calvinists grant, so there is no substantial difference in doctrine upon this point.
The Catholic Church absolutely rejects double predestination (which not all Calvinists hold), but seems to only reject limited atonement in certain interpretations. So while this is a rejection of beliefs of some Calvinists, it wouldn't hit all of Calvinist theology.
However, the big distinctive heresy--or, if you'd prefer, error--of Calvinism according to the Catholic Church is not either of those two things. As noted, double predestination isn't believed by all Calvinists, and some Calvinists have an interpretation of Limited Atonement that is in line with Catholic belief. The thing about Calvinism that the Catholic Church (and, as far as I can tell, non-Calvinists in general) reject is eternal security. Eternal security, which is a portion of the Perseverance of the Saints in the five points of Calvinism, asserts that upon becoming a Christian, no one can lose their salvation, and should anyone deconvert or fall away, it only shows they were never a true Christian to begin with. Therefore, in eternal security anyone who is a true Christian--at least a Christian as defined by those who espouse eternal security--can be assured of their salvation. This idea was rejected by the Catholic Church (Council of Trent, Session 6):
No one, moreover, so long as he exists in this mortal state, ought so far to presume concerning the secret mystery of divine predestination, as to determine for certain that he is assuredly in the number of the predestinated; as if it were true, that he who is justified, either cannot sin any more, or if he do sin, that he ought to promise himself a certain repentance; for except by a special revelation, it cannot be known whom God hath chosen unto Himself.
Indeed, for as much as predestination is viewed as the distinctive Calvinist belief in popular culture, it seems to me that eternal security is the distinctive belief that sets Calvinists apart from others; I've never seen a Calvinist reject it, and there are very few non-Calvinists that accept it.