A reliance on proof texts
It is quite common to support a point by quoting a verse. I do it myself. This assumes that both the person quoting the verse and those listening understand its meaning in its context. This context consists of more than just the surrounding text of the verse but also includes the larger context of the entire Bible, historical and cultural information, and even the interpretative history of the church. It is not the actual words that support the point, but the meaning behind the words. Too often verses are quoted for the meaning that the speaker thinks the words have and this meaning is divorced from the proper context. A growing biblical illiteracy within the church can only increase this type of usage.

Giving a quote from a well known source is not unique to the Christian community. It possess the capability of clearly communicating more meaning with less effort than explaining an idea due to the shared understanding of the source. I am currently reading a book about the Enlightenment. The philosophes during that time period frequently quoted from the classics in their writings. Their education was based around learning Greek, Latin, and the classics so it was a shared intellectual heritage. Upon reading one of these references, the reader would recall the passage it came from and its meaning.

The danger inherent in this is when the reader or writer is unaware of the context but attributes some other meaning to it. Combine a tendency toward proof-texting with a lack knowledge about the Bible as a cohesive whole and I think it is possible to see some of the groundwork being laid for poor uses of 'biblical'. A verse from the Bible can now take on a shared meaning that has little to do with its meaning in context. There was a recent paper in the Journal of Communication that dealt with quotes being used out of their natural context. One of the main points of the paper was that an improper understanding of the context-less quote makes it difficult to recover the true meaning when it is placed back in its original context.

Exaggerating the supernatural character of the Bible
One result of the Enlightenment was a skepticism about the supernatural character of the Bible and about the supernatural in general. During times of controversy it is natural for opposing sides to harden their positions. This is reflected in the church (especially the church in America) during this time by the exaggeration of the divine nature of the Bible at the expense of its human nature. The role of the human writers was downplayed or ignored and I think this created an interesting side effect.

If a text is written by an infinite being, then it should be able to possess an infinite amount of meaning (ignoring Shannon's law for the moment). There could be all sorts of codes embedded in the text. Every detail could have a vital lesson to teach. With human writing, we write to communicate and the meaning we seek to communicate is usually the only purpose of the writing. By this I mean that there is a single meaning to the text and everything in that discourse serves to develop that meaning. It is not the case that every sentence or phrase possesses some knowledge that must be mined for its independent content. With a wholly divine text, some read it as a richly-woven literal allegory - an interesting paradox. It is this type of approach that results in reading a verse that mentions seven different types of food and seeing a secret, divine message in that detail. (And then creating a health bar with that information.) I do not mean to imply that anyone who stresses the divine nature of the Scripture also sees secret meaning in narrative details. I think it is a contributing factor though.

Extreme distrust in the tradition of the church
The distrust of church tradition is an artifact of the Reformation and is common in many Protestant denominations in varying degrees. The most extreme form is an outright rejection of the study of church history and the theological works of the past. This is justified in a few different ways, but a common one is the idea that there is no need for anything other than the Bible and the works of the past are actually unhelpful in understanding and applying God's revelation. Those who believe and practice this effectively cut themselves off from two thousand years of theological discourse. This has multiple negative effects, but there are two important ones that I want to mention in this discussion.

First, it removes the constraining effect of the tradition on the church. What is orthodox theology? To a large extent it is defined or framed by the creeds developed by the church down through the ages. A flow of orthodox interpretations has developed. This allows us in the current day to test our interpretations and see if they lie outside of this flow. Not that tradition is authoritative but it should make us question a new interpretation that is outside of our historical understanding of theology.

Second, and perhaps more obvious than the first one, not knowing the history of the church will result in Christians repeating the mistakes of the past. Knowledge of how others have struggled with understanding a text or applying a biblical principal allows us to avoid some of the pitfalls of hermeneutics and it should also keep us humble about our conclusions. I am convinced that the ignorance of the American church about the history of eschatological doctrine has led to this present "Left Behind" craziness. It also prevents us from working through current issues with a proper historical context which can lead to 'biblical' being used in odd ways.