One such way is to distinguish between inerrancy and infallability. Inerrancy is the view that scriptures are without factual error and even that the translation of scripture is guided by God so so as to make even the English translation of the work 100% without error in translation and by extension impossible to misinterpret because it is in clear and plain English (at the most extreme holding of the view.)
Infallability on the other hand is the view that the truths that The Bible is teaching are without error - in other words, the moral of the stories are true. One needed throw the baby out with the bath water by saying if you dispense with one, you dispense with the other. It is possible to say that the bible remains infallable while not being inerrant. In fact, in some ways, dispensing with inerrant can strengthen beliefs in that a factual error can now be tolerated.
For example, we know that ancient peoples believed that the earth is flat and that you could fall off the earth if you went to it's edge. Were Biblical writers to believe that the earth were flat, this would be consistent with the view of cosmology that all other ancient peoples held. Were they to write down that the earth was flat in verses like Isaiah 11:12, Revelation 7:1, Psalm 75:3 and other verses, this would again be consistent with all ancient peoples' worldview. With a hard line on biblical inerrancy this becomes problematic. Either you must claim that ancient writers posessesed special revelation and understanding that all other ancient peoples did not posess, or that the earth is actually flat (as some flat-earthers do). If you dispense with biblical inerrancy however, you then have the freedom to believe that The Bible does in fact record a flat earth and we now know that this view is wrong, yet The Bible can still retain all of it's moral truths and continue to be divinely inspired and useful for teaching, rebuking and training in Christ.
Similarly, were a translator to make a mistake (or mistakes) or were entire sections of scripture to have been missing or lost for many years, no serious issue is posed if inerrancy is dispensed with while infallability maintained. It allows humans to be human and make mistakes and allows God to be God and remain perfect.
It also potentially opens up entirely new ways of looking at scripture. For example, the framework view of Genesis in which you can retain a literal meaning and interpretation of Genesis while recognizing that the events recorded may never have actually happened due to factual errors. This frees the reader to consider things like Panbabylonism and how comparing and contrasting creation stories might actually teach us more about God and our faith.
Likewise, it allows us to consider that perhaps we are mistranslating arsenokoites and malakos (typically translated as homosexuals) and that we don't actually know what it means or that we lack context when reading Romans' purported prohibition on homosexuality and that Paul was addressing homosexuality as a religious practice.
By my maintaining that The Bible is infallable but not inerrant, the PCUSA can maintain that it is divinely inspired while still teaching that we can come to the wrong conclusion because transmission of this divine inspiration is not supernaturally preserved (nor is our reception and understanding of it) can be corrupted by our humanity and our fallen nature. It allows us to realize that The Bible was written to an audience of Middle Easterners 2000+ years ago and that can lead to some interesting differences in understanding that we ought to account for. Inerrancy really inhibits most or all of the above leeway afforded to the reader otherwise.