We are told, for example, that using a vernacular language in the liturgy is a Good Idea because Jesus used the vernacular Aramaic at the Last Supper. On the other hand, it is countered, it is good to use a special liturgical language in the liturgy because Jesus used the liturgical Hebrew at the Last Supper.
We are told that the priest should face the people at Mass because Jesus faced His disciples at the Last Supper. Nonsense, comes the counter-argument, it is certainly appropriate for the priest to face East because at the Last Supper Jesus and His disciples all faced East together.
We are told that Communion should be given in the hand, because that's how Jesus distributed the first Holy Communion at the Last Supper. On the other hand, we are told that it's unlikely that our Lord placed the sacred Species into the disciples' hands but rather, according to ancient Semitic practice, directly into their mouths.
I've even seen, very recently, that it is a Good Idea to come to Mass plainly dressed, because of course Jesus was plainly dressed at the Last Supper. On the other hand, the counter-argument goes, the Passover was a very special feast for the Jews and it is impossible to think that the participants, much less the one presiding, would not have dressed in their finest.
Well, to state the obvious, none of us were there. We don't know what language our Lord spoke at the Last Supper, nor what He wore, nor which way He faced, nor how He distributed Holy Communion. At best, we have more or less probable guesses based on historical research.
That being said, I think it fairly likely that He celebrated the Last Supper in the non-vernacular Hebrew, facing East with His disciples, "vested" in appropriately non-ordinary clothing, and may very well have placed at least the Consecrated Bread directly into the mouths of the disciples (indeed, I can easily imagine Him distributing both sacred species by intinction as well, following ancient custom). So at the very least traditional Catholic practice is in no way undermined and indeed is probably supported by recourse to the likely actions at the Last Supper. But that is the most that anybody could say, that certain things are more or less likely based on historical research. Because none of the eyewitnesses give us any of these details.
In the end, a lot of these appeals to the Last Supper are rendered invalid on other grounds. There is absolutely no reason whatsoever that the precise details of the Last Supper, even if we had them, should be used to dictate how the Mass is celebrated today. There are many things that have quite rightly changed in their details from the way they were done in the earliest Church versus the way they are done today. As Pope Pius XII states in Mediator Dei §63:
Clearly no sincere Catholic can refuse to accept the formulation of Christian doctrine more recently elaborated and proclaimed as dogmas by the Church, under the inspiration and guidance of the Holy Spirit with abundant fruit for souls, because it pleases him to hark back to the old formulas. No more can any Catholic in his right senses repudiate existing legislation of the Church to revert to prescriptions based on the earliest sources of canon law. Just as obviously unwise and mistaken is the zeal of one who in matters liturgical would go back to the rites and usage of antiquity, discarding the new patterns introduced by disposition of divine Providence to meet the changes of circumstances and situation.