Can non-Catholics be saved?

Yes, absolutely, but never as non-Catholics.  This is the problem with the Second Vatican Council:

"Finally, those who have not yet received the Gospel are related in various ways to the people of God. In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh. On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues. But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Mohammedans, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things, and as Saviour wills that all men be saved. Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience. Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life. Whatever good or truth is found amongst them is looked upon by the Church as a preparation for the Gospel. She knows that it is given by Him who enlightens all men so that they may finally have life. But often men, deceived by the Evil One, have become vain in their reasonings and have exchanged the truth of God for a lie, serving the creature rather than the Creator. Or some there are who, living and dying in this world without God, are exposed to final despair. Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, "Preach the Gospel to every creature", the Church fosters the missions with care and attention." (Lumen Gentium, #16)

The above text from Vatican II changes absolutely nothing of the Catholic faith, nor could it ever do so.  (It would equivalent to saying that 2 + 2 = 5.)  If the above text, poorly worded as it is, teaches that non-Catholics can be saved as non-Catholics, then the text is teaching manifest, public heresy, which would mean that Pope Paul VI, when he signed that document would have excommunicated himself, and the sedevacantist position would be the correct one.  If anyone reads the text as teaching that non-Catholics can be saved as non-Catholics, he/she is guilty of manifest, public heresy and is no longer a Catholic, but an excommunicated heretic.

The only way to reconcile the above text with the immutable and absolute Truths of the Catholic Faith is to say that those who "sincerely seek God" will find Him via "the Gospel," and "moved by grace," they will renounce their former false religions and convert to the One True Faith and the One True Church, outside of which no one at all will be saved.  No other readings of the above text can be permitted.  This is the present error of the current Roman Pontiff, Pope Benedict XVI, in that he allows heretical readings of Vatican II, based upon the defects that the Council Fathers allowed to occur in the Vatican II texts.

A new Syllabus of Errors is needed.  More on that later.

Vatican II affirmed the Council of Florence.

 From the "Dogmatic Constitution on the Church - Lumen Gentium":
This Sacred Council accepts with great devotion this venerable faith of our ancestors regarding this vital fellowship with our brethren who are in heavenly glory or who having died are still being purified; and it proposes again the decrees of the Second Council of Nicea, the Council of Florence and the Council of Trent. And at the same time, in conformity with our own pastoral interests, we urge all concerned, if any abuses, excesses or defects have crept in here or there, to do what is in their power to remove or correct them, and to restore all things to a fuller praise of Christ and of God. Let them therefore teach the faithful that the authentic cult of the saints consists not so much in the multiplying of external acts, but rather in the greater intensity of our love, whereby, for our own greater good and that of the whole Church, we seek from the saints "example in their way of life, fellowship in their communion, and aid by their intercession." On the other hand, let them teach the faithful that our communion with those in heaven, provided that it is understood in the fuller light of faith according to its genuine nature, in no way weakens, but conversely, more thoroughly enriches the latreutic worship we give to God the Father, through Christ, in the Spirit. (Lumen Gentium, 51)
In addition, Lumen Gentium referenced, without any comment, the 1949 Holy Office letter to Father Feeney, which was the only such reference made in all the 16 documents of the Second Vatican Council:

That letter stated:
Accordingly, the Most Eminent and Most Reverend Cardinals of this Supreme Congregation, in a plenary session held on Wednesday, July 27, 1949, decreed, and the august Pontiff in an audience on the following Thursday, July 28, 1949, deigned to give his approval, that the following explanations pertinent to the doctrine, and also that invitations and exhortations relevant to discipline be given:
We are bound by divine and Catholic faith to believe all those things which are contained in the word of God, whether it be Scripture or Tradition, and are proposed by the Church to be believed as divinely revealed, not only through solemn judgment but also through the ordinary and universal teaching office (<Denzinger>, n. 1792).
Now, among those things which the Church has always preached and will never cease to preach is contained also that infallible statement by which we are taught that there is no salvation outside the Church.
However, this dogma must be understood in that sense in which the Church herself understands it. For, it was not to private judgments that Our Savior gave for explanation those things that are contained in the deposit of faith, but to the teaching authority of the Church.
Of course, the First Vatican Council declared:
Pope Pius IX, Vatican Council, Session 3, Chapter 4, #14, ex cathedra: "Hence, too, that meaning of the sacred dogmas is ever to be maintained which has once been declared by Holy Mother Church, and there must never be any abandonment of this sense under the pretext or in the name of a more profound understanding."

Pope Pius IX, Vatican Council, Session 3, Canon 4, ex cathedra: "If anyone says that it is possible that at some time, given the advancement of knowledge, a sense may be assigned to the dogmas propounded by the church which is different from that which the church has understood and understands: let him be anathema."
Therefore, anyone who asserts that Vatican II contradicted the Council of Florence must also conclude that Vatican II contradicted itself, as well as the First Vatican Council; in that respect, it is pointless for dissenters to "appeal" to "Vatican II" as having overturned any Catholic dogma, which, of course, the Council never claimed to ever be doing.

Vatican II -- Is the glass "half-full" or "half-empty"?

Consider this text  from the "Decree on Ecumrnism - Unitatis Redintegratio":
It follows that the separated Churches and Communities as such, though we believe them to be deficient in some respects, have been by no means deprived of significance and importance in the mystery of salvation. For the Spirit of Christ has not refrained from using them as means of salvation which derive their efficacy from the very fullness of grace and truth entrusted to the Church. (Unitatis Redintegratio, 3)
Now, consider this passage from Sacred Scripture:
Just so, I tell you, there will be more joy in heaven over one sinner who repents than over ninety-nine righteous persons who need no repentance. 
"Or what woman, having ten silver coins, if she loses one coin, does not light a lamp and sweep the house and seek diligently until she finds it? 
And when she has found it, she calls together her friends and neighbors, saying, `Rejoice with me, for I have found the coin which I had lost.' 
Just so, I tell you, there is joy before the angels of God over one sinner who repents." (Luke 15:7-15)
While some (such as the SSPX) will read Unitatis Redintegratio as stating that Protestant sects and the Orthodox Churches are now an "ordinary means" to salvation and eternal life, the fact is that we can read the text as saying that those sects and Churches, even though they deny the Primacy of the Vicar of God, nonetheless, have a valid, sacramental Baptism within their communities.  Therefore, an infant who is validly baptized, and especially one who dies before the Age of Reason, will, without any doubt whatsoever, go to Heaven, and who could ever argue which the fact that such was both "significant and important"?!

The problem is, of course, concerning the state of a baptized infant who survives to the Age of Reason and beyond.  The Catholic Church, of course, still teaches (and always will teach until the Second Coming of Christ) that:
Can. 868 §1. For an infant to be baptized licitly:
1º the parents or at least one of them or the person who legitimately takes their place must consent;
there must be a founded hope that the infant will be brought up in the Catholic religion; if such hope is altogether lacking, the baptism is to be delayed according to the prescripts of particular law after the parents have been advised about the reason.
§2. An infant of Catholic parents or even of non-Catholic parents is baptized licitly in danger of death even against the will of the parents.
Vatican II -- universal salvation?

Unless one is prepared to say that the Council was teaching the existence of a "null set" when it referred to those who "are exposed to final despair," then, no, Vatican II did not teach that everyone would be saved.

We ought to presume the eternal loss of all non-Catholics.

Pope Pius IX infallibly teaches us as much:

15. Condemned Error:  Every man is free to embrace and profess that religion which, guided by the light of reason, he shall consider true. -- Allocution "Maxima quidem," June 9, 1862; Damnatio "Multiplices inter," June 10, 1851.

16. Condemned Error:  Man may, in the observance of any religion whatever, find the way of eternal salvation, and arrive at eternal salvation. -- Encyclical "Qui pluribus," Nov. 9, 1846.

17. Condemned Error:  Good hope at least is to be entertained of the eternal salvation of all those who are not at all in the true Church of Christ. -- Encyclical "Quanto conficiamur," Aug. 10, 1863, etc.

18. Condemned Error:  Protestantism is nothing more than another form of the same true Christian religion, in which form it is given to please God equally as in the Catholic Church. -- Encyclical "Noscitis," Dec. 8, 1849. 

And, of course, the Syllabus of Errors was infallible:

Question is for you, dear Reader, "Do you want to embrace the 'modernist majority' or do you want to adhere to the One True Religion with all your 'mind, body, and soul'?"  The One and Triune God, a Perfect Being, is above all, Truth, which makes the answer self-evident.