Just as a general caveat before saying anything else here, one of the main problems in answering this is that we don't really have good records of the views of the "average" Israelite/Judean on issues like this. Almost every piece of literature we have that's pertinent to the subject comes from a sort of scribal elite that was lucky enough to be educated, and lucky enough for their writings to have been copied and survive through the ages; and of course, if we do have some off-hand notes about the wider populace's views here, these still come from this elite—in the way they chose to present them, with all the their biases and motives for this, etc.

On another kind of general note, if we know anything from ancient Israelite/Judean history—and this is true of some other cultures, too—we know that the wider populace can have practices and values that differ drastically from the way they're presented in "official" accounts. For the Israelites/Judeans in particular, archaeological and other literary evidence can suggest that things like child sacrifice, polytheistic worship, and magical practice could be more "mainstream" than the devious heresy they're often made out to be. (The abundant evidence of Judean pillar figurines is often a common example used to illustrate this.)

With those things in mind, it's just so hard to say what the average Jew of the time leading up to the first century CE thought about the gamut of Biblical literature and its truth. In terms of more skeptical views that may have been held, for some reason the first thing that comes to mind here—though, really, this could just be another more general illustration—is something that comes from one of the Psalms. I certainly don't share this view, but the opening line of Psalm 14 is "Fools say to themselves, 'There is no God'"; and it's actually been widely recognized by Biblical scholars that the "fools" the Psalmist had in mind here weren't simply outsiders who didn't believe in the Jewish God, as many might be inclined to interpret it, but rather that it was aimed at Israelites/Judeans themselves—perhaps even those who did affirm the existence of the Jewish God, but simply doubted his power or the extent of his intervention into our world and its history.

So this could certainly align with Israelites/Judeans who looked toward various Biblical literature and suspected that some or many of the stories within it had the distinct whiff of being tall tales (even for those who still affirmed the existence of the Jewish God).

But that only covers the most skeptical of the populace. There's still the issue of how Biblical literature would be interpreted by those who were, in short, more pious. And again, on a more general note, in your title you asked about views on "inerrancy," and here I think it's important to note that the earliest discernible views on the issue of divine Biblical inspiration were held not by virtue of the fact that there was a codified Bible itself (e.g. "the stories in the Old Testament are inerrant because they're from the Bible"), but because of the nature of the content of particular pieces of Biblical literature. For example, the Law of Moses in the Torah proclaims to have been authored by God himself; and in later Jewish tradition the entirety of the Torah (Genesis through to Deuteronomy) was thought to have been revealed by God. Further, the visions and predictions which are recorded in the prophetic literature in the Bible proclaim to be of divine origin.

In other words, when it comes to what early Jews thought of the accuracy of Biblical stores, there may be some latitude here when it comes to Biblical literature that's more historical in nature, and didn't explicitly claim to be of divine origin.

Two other things here: leading up to the time of Jesus, there was a preponderance of Jewish literature that purported to be written by famous figures known from the Hebrew Bible: this is called the pseudepigrapha. Now, the word "pseudepigrapha" itself implies that these texts were falsely written in these figures' names; and scholars universally affirm that most of the texts that are grouped into this category weren't actually written by who they claim to have been written by. So at least to the actual authors of these texts, they themselves were obviously aware that what they were writing wasn't strictly "true" in many senses. However, we shouldn't downplay the fact that although they were clearly engaged in a kind of fictionalizing here, the very reason many would choose to do this is because they did have views that they wholeheartedly believed to be true: these authors simply appropriated these renowned figures as mouthpieces that could be used to express their own views more authoritatively, and to promulgate them more widely.

And audiences were often all too willing to accept these as genuine. (There are any number of academic studies of Jewish and Christian pseudepigraphy. First and foremost, James Charlesworth's The Old Testament Pseudepigrapha is a standard anthology of Jewish [and some Christian] pseudepigraphical works. See also the work of scholars like John Collins [like the chapter "Pseudepigraphy" in his Apocalypse, Prophecy, and Pseudepigraphy], and Bart Ehrman's Forgery and Counterforgery for Christian pseudepigraphy in particular. Also, Mroczek's The Literary Imagination in Jewish Antiquity has some good stuff.)

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As for the second thing I want to point to, though, there's a particularly interesting little passage that's found in a book written by the first century Jewish philosopher and Biblical interpreter Philo of Alexandria. Now, Philo was famous in Jewish and Christian tradition for his allegorism: his interpretation of individual Biblical passages as concealing some deeper hidden allegorical meaning—usually some sophisticated philosophical or ethical principle that's radically different from what appears to be expressed on the "surface" of the text.

I'll get back to how exactly Philo's allegorism worked in a second; but for now, I'll just quote the relevant section of Philo itself, from his On the Migration of Abraham (and note that Philo is talking about the laws of Moses here, from the Torah—and about the observance of the Sabbath in particular):

There are some who, regarding laws in their literal sense in the light of symbols of matters belonging to the intellect, are overpunctilious about the latter, while treating the former with easy-going neglect. Such men I for my part should blame for handling the matter in too easy and off-hand a manner: they ought to have given careful attention to both aims, to a more full and exact investigation of what is not seen and in what is seen to be stewards without reproach. . . . It is quite true that the Seventh Day [=Sabbath] is meant to teach the power of the Unoriginate [=God] and the non-action of created beings. But let us not for this reason abrogate the laws laid down for its observance and light fires or till the ground or carry loads or institute proceedings in court or judge or demand the restoration of deposits or recover loans or do all else that we are permitted to do as well on days that are not festival seasons.

It is true also that keeping of festivals is a symbol of gladness of soul and of thankfulness to God, but we should not for this reason turn our backs on the general gatherings of the year’s seasons. It is true that receiving circumcision does indeed portray the excision of pleasure and all passions, and the putting away of the impious conceit, under which the mind supposed that it was capable of begetting by its own power: but let us not on this account repeal the law laid down for circumcision. Why, we shall be ignoring the sanctity of the Temple and a thousand other things, if we are going to pay heed to nothing except what is shown us by the inner meanings of things.

No, we should look on all these outward observances as resembling the body, and their inner meanings as resembling the soul. It follows that, exactly as we have to take thought for the body, because it is the abode of the soul, so we must pay heed to the letter of the laws. If we keep and observe these, we shall gain a clearer conception of those things of which these are the symbols; and besides that we shall not incur the censure of the many and the charges they are sure to bring against us.

Basically, Philo is criticizing some band of extreme allegorists, who are so caught in trying to discern the hidden spiritual dimension of the laws in the Torah that they ignore and/or downplay what the laws actually command on the surface level!

One of the reasons I mention this in particular is because many people who are at least tangentially familiar with Philo of Alexandria, as well as with some of the early Christian interpreters that Philo influenced, might actually have somewhat of a mistaken impression of how their interpretation worked. There's a common idea that they too often rejected the surface-level, "literal" meaning of the Biblical texts, preferring instead these deeper allegorical ones. But as can be seen in the lines quoted above, Philo is at pains to emphasize that both senses of interpretation should work together: "they ought to have given careful attention to both aims."

And I think Philo's perspective here is in many ways illustrative of early Jewish and Christian Biblical interpretation as a whole.

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I've just about hit the character limit; I've continued in the comment below.

This is an interesting question, one I've often wondered on many religions. Does anyone have any good reading material on the history of actual Faith? Did Vikings think Odin would help them in the year 1000? Did any Romans fear Jesus because they believed he might have had those abilities? I have to wonder how many primary sources of that kind there might be, it would be dangerous during most time periods. I hope we both get an answer, OP!

I'm not a historian but I know a bit about this stuff...

When Jesus was alive there were several groups of Jews: the Pharisees, Sadducees, and Essenes were three of the most well-known. The Sadducees were strict adherents to the Torah and believed in the importance of the priestly caste and the critical nature of the Temple to Judaism, but they also were ok with incorporating then-modern elements of society into their lives. The Pharisees weren't as strict adherents to the Torah as written (they felt it was open to interpretations and so on). The Essenes were a kind of crazy group that had very strict laws that sometimes differed from the Torah and they didn't last very long, but we know a lot about them because we've found their writings near the Dead Sea (the Dead Sea Scrolls). There's more detail here: http://www.jewishvirtuallibrary.org/pharisees-sadducees-and-essenes

Remember that when Jesus was alive the second Temple actually existed (it was destroyed a few decades later) and people prayed there and sacrificed animals there and all that stuff. So there were many facets to Judaism that were political in nature in addition to religious: Different religious groups had opinions on the role of the Torah, but they also had opinions on what role the Second Temple and priests and the various rulers should play in daily and religious life. But a lot of that political stuff became moot once the Temple fell.

Another thing to keep in mind is that modern Jews consider the Bible to consist of three parts: the Torah, Prophets and Writings, with several books in each; but the modern consensus as to which books constitute the Bible wasn't really formed until after Jesus' time. In addition, the modern beliefs of Jews didn't become codified in the way that Orthodox Jews think of them today until the Talmud was written a few centuries later. I bring this point up because different groups of people can reasonably believe the same group of writings to be "inerrant and literal truth" in different ways. Kosher laws are a good example -- the Torah forbids you from cooking a goat in its mother's milk, but modern (Orthodox) Judaism extends that to prohibitions on combining meat and diary (this is codified in the Talmud, which came about centuries after Jesus). The Torah doesn't exactly say anything about a prohibition on combining all meat and dairy products, but the Talmud maintains that this is what it means. So like I said, "inerrant and literal truth" is open to interpretation and modern Jews can disagree on how or whether men are capable of interpreting it.