Critics that doubt modern bibles are reliable copies of original writings are nothing new, and there is nothing original that comes out of this guy's mouth. The truth is, we do rely on copies (just like every work from this time period) and some copyists were careless or even tried to alter the text deliberately. However to say:
"We simply cannot be sure that we have reconstructed the original text accurately" and "we only have error-ridden copies" - is simply not true and does not hold up to close scrutiny.
This is why scores of Hebrew, Aramaic and Greek scholars who have examined (and continue to examine) existing texts agree that there is not a single work of antiquity that has been so accurately transmitted. For example, one group - the Masoretes were a professional, highly skilled and meticulous group of copyists. When the Dead Sea Scrolls were discovered the Masoretic texts were compared to Bible scrolls that were written a thousand years earlier it was found they were essentially the same documents with only minor spelling differences. This is why one of the scholars that examined the scrolls said it "provides irrefutable proof that the transmission of the biblical text through a period of more than one thousand years by the hands of Jewish copyists has been extremely faithful and careful."
The same is true for the hundreds + Greek texts all in agreement (research Chester Beatty collection for example) in which Matthew is found, some of which date to within 100 years of the originals. "No other ancient book has anything like such early and plentiful testimony to it's text, and no unbiased scholar would deny that the text that has come down to us is substantially sound" -Sir Frederic Kenyon.
TL;DR:
There are literally thousands of manuscripts extant that when cross-referenced allow us to establish the Bible Canon (what may and may not be included)
To say we don't have any accurate copies is nonsense and there are scores of scholars that disagree with Bart Ehrman.