First off, Pope Leo XIII said this about the inerrency of Scripture:
For all the books which the Church receives as sacred and canonical are written wholly and entirely, with all their parts, at the dictation of the Holy Spirit; and so far is it from being possible that any error can coexist with inspiration, that inspiration not only is essentially incompatible with error, but excludes and rejects it as absolutely and necessarily as it is impossible that God Himself, the supreme Truth, can utter that which is not true. This is the ancient and unchanging faith of the Church, solemnly defined in the Councils of Florence and Trent, and finally and more expressly formulated by the [First] Council of the Vatican (EB 124-125).
In the light of the errors in great number which can be demonstrated, the above statement is most unfortunate because the standard of Leo XIII damns scripture in the final analysis as nothing less than manmade!
References for examination concerning errors and the rebuttal to the claims of error:
http://www.infidels.org/library/modern/paul_carlson/nt_contradictions.html
http://www.religioustolerance.org/chr_bibl.htm
Of the first class, that of unconscious errors, there are five sorts:
Errors of the eye
, where the sight of the copyist confuses letters or endings that are similar, writing e.g. E for S ; O for Q ; A for L or D ; P for TI ; PAN for TIAN ; M for LL . Here should be named
homoeoteleuton, which arises when two successive lines in a copy end in the same word or syllable and the eye catches the second line instead of the first and the copyist omits the intervening words as in Codex Ephraemi of John 6:39.
Errors of the Pen
. Here is classed all that body of variation due to the miswriting by the penman of what is correctly enough in his mind but through carelessness he fails rightly to transfer to the new copy. Transposition of similar letters has evidently occurred in Codices E, M, and H of Mark 14:65, also in H2 L2 of Acts 13:23.
Errors of Speech
. Here are included those variations which have sprung from the habitual forms of speech to which the scribe in the particular case was accustomed and which he therefore was inclined to write. Under this head comes "itacism," arising from the confusion of vowels and diphthongs, especially in dictation. Thus, i is constantly written as ei and vice versa; ai for e ; h and i for ei ; h and oi for u ; o for w and e for h . It is observed that in Codex Sinaiticus we have scribal preference for i alone, while in Codex Vaticanus ei is preferred.
Errors of Memory
. These are explained as having arisen from the "copyist holding a clause or sequence of letters in his somewhat treacherous memory between the glance at the manuscript to be copied and his writing down what he saw there." Here are classed the numerous petty changes in the order of words and the substitution of synonyms, as
eipen for efh , ek for apo , and vice versa.
Errors of Judgment
. Under this class Dr. Warfield cites "many misreadings of abbreviations, as also the adoption of marginal glosses into the text by which much of the most striking corruption which has entered the text has been produced." Notable instances of this type of error are found in John 5:1-4, explaining how it happened that the waters of Bethesda were healing; and in John 7:53-8:12, the passage concerning the adulteress, and the last twelve verses of Mark.
Turning to the second class, that of conscious or intentional errors, we may tabulate:
Linguistic or rhetorical corrections
, no doubt often made in entire good faith under the impression that an error had previously crept into the text and needed correcting. Thus, second aorist terminations in a are changed to o and the like.
Historical Corrections
. Under this head is placed all that group of changes similar to the case in Mark 1:2, where the phrase "Isaiah the prophet" is changed into "the prophets."
Harmonistic Corrections
. These are quite frequent in the Gospels, e.g. the attempted assimilation of the Lord's Prayer in Luke to the fuller form in Matthew, and quite possibly the addition of the words "of sin" to the phrase in John 8:34, "Every one that doeth sin is a slave." A certain group of harmonistic corruptions where scribes allow the memory, perhaps unconsciously, to affect the writing may rightly be classed under (4) above.
Doctrinal Corrections
. Of these it is difficult to assert any unquestioned cases unless it be the celebrated Trinitarian passage (King James Version, 1 John 5:7,8a) or the several passages in which fasting is coupled with prayer, as in Matthew 17:21; Mark 9:29; Acts 10:30; 1 Corinthians 7:5.
Liturgical Corrections
. These are very common, especially in the lectionaries, as in the beginning of lessons, and are even found in early uncials, e.g. Luke 8:31; 10:23, etc.
An older reading is preferable to one later, since it is presumed to be nearer the original. However, mere age is no sure proof of purity, as it is now clear that very many of the corruptions of the text became current at an early date, so that in some cases it is found that later copies really represent a more ancient reading.
A more difficult reading, if well supported, is preferable to one that is easier, since it is the tendency of copyists to substitute an easy, well-known and smooth reading for one that is harsh, unusual and ungrammatical. This was commonly done with the best of intentions, the scribe supposing he was rendering a real service to truth.
A shorter is preferable to a longer reading, since here again the common tendency of scribes is toward additions and insertions rather than omissions. Hence arose, in the first place, the marginal glosses and insertions between the lines which later transcribers incorporated into the text. Although this rule has been widely accepted, it must be applied with discrimination, a longer reading being in some cases clearly more in harmony with the style of the original, or the shorter having arisen from a case of homoeoteleuton.
A reading is preferable, other things being equal, from which the origin of all alternative readings can most clearly be derived. This principle is at once of the utmost importance and at the same time demands the most careful application. It is a sharp two-edged-sword, dangerous alike to the user and to his opponents.
A reading is preferable, says Scrivener, "which best suits the peculiar style, manner and habits of thought of an author, it being the tendency of copyists to overlook the idiosyncrasies of the writer. Yet habit or the love of critical correction may sometimes lead the scribe to change the text to his author's more usual style as well as to depart from it through inadvertence, so that we may securely apply the rule only where the external evidence is not unequally balanced."
A reading is preferable which reflects no doctrinal bias, whether orthodox on the one side or heretical on the other. This principle is so obvious that it is accepted on all sides, but in practice wide divergence arises, owing to the doctrinal bias of the critic himself.
http://skeptically.org/newtestament/id10.html
And a fair rebuttal needs to be included from the apologist's side of things: http://www.tektonics.org/lp/nttextcrit.html