- Plenary inspiration and inerrancy of Scripture; there are no historical, scientific, or theological errors anywhere in Scripture (the only so-called "exception" are minor copyist errors, which are a different issue). Many today are of the heretical camp known as "Modernists" and "Liberals" who cannot accept the idea the Bible is really inspired and thus contains no error, especially since they are of the impression difficulties in the Bible are most logically taken to be actual errors and myths. Unfortunately, these Liberals have entrenched themselves in high enough places as to keep many people confused about the Church's actual (and dogmatic) stance on the subject.
- The "Traditional Latin Mass" is an eternal treasure and ideal form of Liturgical worship for the Latin Rite of the Catholic Church. When Pope Benedict issued the Motu Proprio allowing any priest to say the TLM, he made it clear in his Accompanying Letter: "In the history of the liturgy there is growth and progress, but no rupture. What earlier generations held as sacred, remains sacred and great for us too, and it cannot be all of a sudden entirely forbidden or even considered harmful." The main complaint "traditionalists" have with the "New Mass" (Novus Ordo) created in 1970 by Paul VI is not in regards to it's validity - the New Mass is certainly valid since the Church cannot promulgate invalid Sacraments, and it offers to God the eternal glory of Christ's Sacrifice (so anyone who says otherwise is actually in heresy) - the 'issue' is that this mass was not part of a liturgical heritage that has been passed down and perfected through 'organic development', but rather the invention of a modern liturgical committee who basically invented a mass on the spot and with a very limited outlook (and some even say with malicious intent). The content of the "old Mass" has been perfected over time to express all the important and unique facets that define us as Catholics, while much of these prayers and gestures and music have been tossed, forgotten, or downplayed in the "new Mass," with a sad loss of heritage and richness of prayer and theology. To hate the TLM, which many liberals (sadly) do - precisely because it is 'too Catholic' for them - is to hate your Catholic heritage and even implicit cooperation with the powers who hate Catholicism and seek to undermine it.
- Every doctrine authoritatively taught in prior Councils and Encyclicals and such is still to be held and maintained today. In other words, no official doctrines have been changed or abandoned, no matter how 'unpopular', 'inconvenient', or what any dissident Catholic says (no matter their authority level). Too often, there are many 'inconvenient truths' of Catholicism - which the Church has maintained regardless of opposition - are those that many today have a hard time accepting, from the liberal theologian who cannot accept Jesus really Resurrected, to the Catholic politician who wants to divorce their faith from their politics, to mainstream layman in the pews who wants to engage in contraception.
- The centrality of the Dogma of the Social Kingship of Christ in Catholic living. Many Catholics today are unaware of this dogma, which states that Christ is not only king of believers and on "spiritual" matters, but that Jesus is in fact King of every person of every nation and His authority and theology influences every aspect of daily living from recreation to economics to civil law to theology. Many are shocked to hear that Christ is King over subjects like civil law and economics because they are taught the 'right way' to live is by "separating Church and State" - what they don't know is that such an idea is condemned by the Church as heresy and undermines Christ's Kingship. But the logic is plain: how can Christian teachings of faith and morals be divorced from one's legal or economical views? Is it suddenly ok to steal because an economics theory allows it or have abortions because a human court permits it? In such situations, the Apostles teach: "We ought to obey God rather than men" (Acts 5:29), meaning God's teachings through the Church trump the teachings of mere human authorities.
- So-called 'little-t' traditions, even if not dogmatic (i.e. 'big-t' Tradition), are none the less very important for maintaining Catholic identity and integrity - in other words, 'little-t' traditions are by no means dispensable, deplorable, or harmful. 'Little-t' traditions are prayers, devotions, art forms, music, etc, that while not absolutely necessary for moral and theological integrity (and can be altered under proper conditions), have been put in place precisely to preserve Catholic identity and culture. For example, the Rosary is a little-t traditional Catholic devotion that is a uniquely Catholic prayer, teaching and fostering uniquely Catholic piety. Externally, little-t tradition is what helps distinguish Catholics from non-Catholics, while internally little-t tradition exists to form the Catholic's mind and soul in how a Catholic is to think and pray. So with the example of the Rosary, while Catholics could abandon this devotion tomorrow without affecting dogma, they would still be negatively affecting Catholic identity and prayer, increasing the risk of Catholic devotion (which sanctifies) being obliterated or replaced by pagan or heretical devotions (which endanger). Another example (of many) is that of holy water, which not only is to help remind us of our Baptismal promises, there are graces attached to the water (by the prayer of the priest), which when used with the proper disposition can cause increase of our sanctification and protection from sin. Sure holy water is not 'necessary' to be Catholic, but it combined with all the other 'little things' adds up to a uniquely Catholic mindset (that in itself fosters sanctification and protection against sin).
In conclusion, it is also worth mentioning that many traditionalists have acted in very uncharitable ways towards their Catholic brothers who are simply not up to speed on traditionalism. This traditionalist triumphalism and arrogance and even verbal attacks have unfortunately scandalized many Catholics, regardless of how 'justified' the traditionalist might have felt. Such an approach is wrong, and does more harm than good. It's an easy mindset for the traditionalist to fall into, but we traditionalists must encourage eachother to not do so. One traditionalist I respect repeatedly emphasized the lack of progress and hypocrisy among many traditionalists was due to the fact they themselves couldn't keep a tight reign on their own sins and weren't themselves working towards an increase in sanctification (James 1:26).
NOTE: So-called "radical traditionalists" (RadTrads) are not really traditionalist or Catholic at all - and must not be confused with traditionalists (as described above) - since RadTrads are characterized as 'radical' precisely because they have indeed gone where no Catholic teaching ever permits, which is to areas like schism from the Pope or even sedevacantism (teaching there has been no Pope for over 50 years).