In Eastern Orthodoxy, when doing a service, do little mistakes really matter, and should they be cause for concern?

Is there any Saint who has spoken about this kind of involuntary mistake? And also about if the Typikon (and all the Holy Services books) should be complied very very precisely (or maybe is more useful to pray much better)?

Why do you call such a mistake "involuntary"? The motive and the path that led to the mistake are important here. If it is negligence and sloth, then by a negligent performance of a church service, we show our disrespect to God, this sin is called blasphemy.

For you, brethren, have been called to liberty; only do not use liberty as an opportunity for the flesh, but through love serve one another (Gal. 5, 13).

Negligence and sloth is, of course, a pandering to the flesh.

When considering the Eucharist itself I appreciate Alexander Schmemann's perspective:

(For the Life of the World, Chapter 2, Part 7)

It is indeed one of the main defects of sacramental theology that instead of following the order of the eucharistic journey with its progressive revelation of meaning, theologians applied to the Eucharist a set of abstract questions in order to squeeze it into their own intellectual framework. In this approach what virtually disappeared from the sphere of theological interest and investigation was liturgy itselfy, and what remained were isolated "moments," "formulas" and "conditions of validity." What disappeared was the Eucharist as one organic, all-embracing and all-transforming act of the whole Church, and what remained were "essential" and "nonessential" parts, "elements," "consecration," etc.

Your question reminded me of exactly this passage, because it you appear to be worried about the legal validity of a service and legal culpability of one who might "mess up". Like Fr. Schmemann says, I think it is first and foremost important to recognize each service as a journey of the Church and not a set of magic words that change the bread and wine into something special (the priest is not Harry Potter and the service books are not spell books). What validates the service is the Holy Spirit and the love present. Note that one of the most curious parts of the litury is "Let us love one another that we may confess, Father, Son and Holy Spirit"; the action of love precedes the dogmatic confession.

That is not to say mistakes in the service aren't detrimental. For instance, kneeling on Sunday or singing the Paschal hymn in the middle of Holy Week is not good, because it violates the how the Church understands those times and uses them to teach us. Also, if a chanter cares nothing for the variation of the services and simply chants the same thing at every service instead of taking the care to learn the cycles then he has failed to love the parishioners by depriving them of the fullness of what the church offers. If on the other hand the parish is trying to learn the services and progress in their understanding in love and under the guidance of their bishop and the teachings of the Church they can do no wrong.

You clarified your question in a comment:

If there are a dogma regarding that, if it is considered a sin, if God and/or The Church focuses on very precisely compliance of Typikon or Orthodox Tradition, if it does not matter a such kind of mistake in generally

Sin, as John wrote, is lawlessness (1 John 3:4). This is also the definition cited in The Longer Catechism of the Orthodox Church, by Metropolitan Philaret. The 20th century Orthodox theologian and monk, Justin Popovic explained this verse:

The law of God is the Gospel: lawlessness is sin. Its [sin's] only law is to be without the law of God and against the law of God. In essence, the law and that which is lawful is only that which is divine and of the Gospel; lawlessness is everything that is in opposition to that which is divine and of the Gospel.

Commentary on the Epistles of St. John the Theologian, (tr. Sebastian Press, 2009), p. 40

In the Gospel, we are commanded to be perfect (Matthew 5:48). In this sense anything we do or fail to do in dishonoring or honoring God and our brothers and sisters through inattention is sinful. The prayers and rubrics in the Typicon were prescribed by our hierarchs for the spiritual benefit of all who read and attend the service, so we fall short of helping our brothers and sisters when we make mistakes in the service through our inattention. But we also fall short when we have an unkind word for them or an unkind thought about them. There is not a special checklist that God maintains that relates specifically to errors of one sort or another.

Indeed, the Typikon is very strict and precise. However, the reality is that all men are error prone.

I've attended many liturgies in many churches and, very rarely, the priest starts reciting or singing the wrong part or the choir starts giving the wrong answer but each and every time this has happened they just stopped and started over correctly. I've never seen in practice a mistake made in the liturgy and not being corrected immediately, even at the cost of spoiling a bit the participants immersion into the rite.