Much debate can arise over Scripture when people agree about what is basically being said, but disagree about the scope to which it should be applied. Consider Ephesians 5:21
Submit one to another out of reverence for Christ.Is this all people to all people, or some people to some people? Both are possible interpretations. I think the context of the verse, and the subsequent examples answer this question, nevertheless there is disagreement between those who advocate all Christians should submit to all other Christians, and those who advocate that Christians are to continue to submit appropriately to others over them.
Or consider the Sermon on the Mount. Some advocate that Jesus is teaching a new way of acting for all men and institutions: abandoning ideas like retaliation and justice and replacing them forgiveness and mercy. Others suggest this is directed at individuals and therefore is inapplicable to the state. Still others may specify that the sermon is even more limited being directed to Jesus' followers. A broad interpretation leads to quite different ideas about the role and extent of government than a narrow interpretation; both camps arguing for contradictory things yet both appealing to Scripture.
Underlying intent is even more subtle, yet very important, and probably open to more disagreement. It is important to establish what kind of situation the Bible is talking to, what are the underlying elements, the foundational concepts. For example the Bible talks a lot about orphans and widows. It seems very natural to extend this to modern orphans and widows, however one should also address why God talks about orphans and widows the way he does: what was the reason for God's concern, and are those concerns applicable to contemporary orphans and widows? They may be, or they may still apply to orphans but not widows, or there may be other categories of people these concerns also apply to.
While there may be valid debate around the breadth of meaning and the underlying intent, getting these wrong may still lead to error, and a key to right meaning is correct focus.