Since time is short, I shall deal with just three, leaving others to propose more of them.
1. Lex orandi lex credendi. Like all clichès, that one has an element of truth. Beliefs that are expressed or logically presupposed by the ancient and established liturgical prayers of the churches with apostolic succession are authentic elements of Tradition, and therefore true. The Fathers of the Church put that fact to good use in the controversies that swirled before and around the great ecumenical councils of the first millennium. In theological debate nowadays, however, LOLC is now more often invoked as a slogan to mean its logical converse: i.e., what is not expressed or logically presupposed by the ancient and established liturgical prayers is not an authentic element of Tradition and therefore, even when not false, at least not binding on believers.
That is nonsense. For one thing, LOLC's converse does not follow from it and, quite arguably, isn't even true. And even if it is true, hardly anybody who thus uses LOLC as a slogan offers any argument that it is is true. At this stage in theological history, the slogan is best dropped. It only gets in the way of assessing the truly pertinent arguments.
2. The Vincentian Canon. This one is a bit more complicated. First, I quote the relevant passage from St. Vincent of Lerins:
Now in the Catholic Church itself we take the greatest care to hold that which has been believed everywhere, always and by all. That is truly and properly 'Catholic,' as is shown by the very force and meaning of the word, which comprehends everything almost universally. We shall hold to this rule if we follow universality [i.e. oecumenicity], antiquity, and consent. We shall follow universality if we acknowledge that one Faith to be true which the whole Church throughout the world confesses; antiquity if we in no wise depart from those interpretations which it is clear that our ancestors and fathers proclaimed; consent, if in antiquity itself we keep following the definitions and opinions of all, or certainly nearly all, bishops and doctors alike.
In its immediate historical context during the early 5th century, that served a useful purpose. It was meant to distinguish the faith of the "catholic" Church (the Church kata holou, "as a whole") from that of various heretical sects which also claimed apostolic origin or validity. St. Irenaeus had made a similar move in his confrontations with the Gnostics of Lyons during the late 2nd century. But nowadays, and with unintended irony, the phrase that which has been believed everywhere, always and by all is taken out of its original context and invoked to reject the distinctive doctrines of that church which has called herself the Catholic Church ever since. After all, it is urged, those doctrines are not believed by Orthodox and Protestants, and therefore are manifestly not "believed everywhere, always, and by all." The not-so-subtle implication is that the Catholic Church must herself not be "the Catholic Church" of which St. Vincent spoke.
That bit of sloganizing too is nonsense. For one thing, it begs the question which church counts as "the" Church and therefore as the Catholic Church. If the Catholic Church is the Church, then whatever validity the VC retains today pertains to her, not to those churches which, for whatever reason, lack full communion with her. And even if the Catholic Church is not the Church, her mere existence as Christianity's largest church leaves other churches in no better a logical position vis-à-vis the VC than she is. So let's drop this slogan too.
3. Scripture and/or Tradition contain all those things belief in which is necessary for salvation. There is a sense in which that too is true. I say "Scripture and/or Tradition" because the truth here is often sloganized, and thus obscured, in exactly the same way by Orthodox as by Protestants. The latter will often tell you that we needn't believe anything that is not to be found explicitly in Scripture; the former will often tell you that we needn't believe anything that is not to be found explicitly in Tradition, typically as expressed through the (Orthodox) liturgy. The not-so-subtle implication is that the Catholic Magisterium's claims for itself are at best superfluous and probably hooey.
The reason that bit of sloganizing is nonsense is that the Catholic Church herself shares the belief thus sloganized, but no more needs to than does draw the implication intended by the sloganizers. She grants that, in Thomas Aquinas' words, Scripture by itself is "materially sufficient" as a repository of saving truth. She has become historically savvy enough to recognize that Scripture is itself a normative, written crystallization of Tradition, so that we may say that Tradition—i.e., all that which is "handed down" from the Apostles as belonging to the Church's faith and life—is materially sufficient as a repository of saving truth. But what is materially sufficient is not thereby formally sufficient. Over time, controversies over interpretation arise and certain ideas develop into doctrines, such as the essence-energies distinction and the Immaculate Conception. If Scripture and Tradition alone were formally sufficient, such things wouldn't happen.
Given that they do, some authority is needed to resolve the controversies and either authenticate or reject the developments. Of course there is disagreement among Christians about the location and identity of that authority. But the sloganizing of the truth in question distracts attention from the need to consider very carefully the question how to locate and identify that authority. Once one acknowledges that, then whatever answer one comes up with, it isn't going to be that the Catholic Magisterium is superfluous and its claims hooey. Mistaken, perhaps; but worthy of the most serious consideration.