There's a theory that Matthew was originally written in Hebrew but then translated to Greek. The book contains many idioms that only make sense in Hebrew. Here's a long but interesting video on this:
https://www.youtube.com/watch?v=tddCNY6U77Y
This is my current understanding of inerrancy according to my research:
It's true that there are many textual variations in the NT manuscripts but most of the errors are minor enough and don't convey anything earth shattering that would challenge the fundamentals of Christian faith. Most of the variations just paraphrase one another like this one:
Matthew 10:14
εκ των ποδων υμων (out of your feet) — א C 0281 33 892 lat
απο των ποδων υμων (away from your feet) — \mathfrak{P}110
των ποδων υμων (of your feet) — rell
http://en.wikipedia.org/wiki/Textual..._New_Testament
There's enough repetition of concepts and doctrine in the NT that makes up for the lacks and addition between the five major groups of manuscripts or between the Critical Text and the Received Text. Also because Greek grammar is so precise, some of the copyist errors can be deduced away. There are also quotes of scripture by early church fathers that lend credence to certain manuscripts over others.
Interestingly enough the OT is a different story because the dead sea scrolls confirm the textual accuracy of the Hebrew in the OT we use today almost word for word.
The early church only had the Old Testament available to them and they did pretty well because they have the same Holy Spirit with them as we do today.
John 10:35
If he called them 'gods,' to whom the word of God came--
and Scripture cannot be set aside--