In some cases, the date of the writing of a text or book of the Bible may not be all that important. For example, we are not at all certain of the date of the writing of the Book of Job. The Psalms, too, are not written in the same time period (Psalm 90, for example, was penned by Moses, who lived much earlier than David). Some books seem deliberately vague regarding such matters. In such cases, we probably should not work too hard at establishing a date of writing when it will be a matter of speculation.
On the other hand, the date of the writing of some books is very important. Some liberal scholars would have us believe that the prophecies of the Bible are not really prophecies at all, but are rather accounts of what has already taken place. The prophecies of Isaiah, for example, are said to be “history,” rather than prophecy. It is very important in such cases that we attempt to establish the time of writing with some degree of certainty.
The date of an epistle can be important because it may give us a clue as to the circumstances out of which the author is writing (for example, before the fall of Jerusalem in 70 A.D. or after?; before the Jerusalem Council in Acts 15 or after?). Knowing how “late” a New Testament epistle is written may help us identify more accurately the error or heresy the author is refuting (e.g. gnosticism).
Having said this, I believe that if the date of the writing is important, God will give us clear indications of when that was. Where the date cannot be established with confidence, I believe that we should not force a date on the text, and interpret it without having a specific setting in time in mind.
Basically, it is my conviction that the Bible is self-explanatory, and that outside materials are not essential to understanding or interpreting it. Outside, background material may be helpful, but is not essential if the Bible itself does not provide it for us.