Dispensationalism is a framework, but the framework itself is only the result of a few basic assumptions. These basic assumptions are wrong, which is why the framework is so complicated.
1 The Jew-Gentile division was permanent, thus:
2 The current Christian priesthood is temporary, thus:
3 The current priesthood must be removed and the Aaronic one reinstated at some point.
The "framework" is really just this three-fold lens. Consequently, most if not all the post-exilic promises of restoration in the prophets are removed from their historical context and applied to the modern state of Israel, and all of the predictions concerning the destruction of Jerusalem in AD70 in Daniel and the New Testament are applied to some future event. This creates incredible confusion, some crazy charts and some even crazier people.
An example: the invasion Israel by Gog and Magog in Ezekiel 38-39 is taken to be a modern invasion of Israel (the identity of the invaders is always taken from the current news headlines). However, the structure of the book and the content of the chapters shows it is a prophecy of the events in the book of Esther (un-walled cities, Haman-Gog / Haman the Agagite, etc), a proposed slaughter and plundering of all Jews between India and Ethiopia. This victory was the vindication of a resurrected Israel before all nations - back then.
The misinterpretation allows authors to write best-selling books about a coming invasion, and republish them every few years with different villains.
Also, since the Revelation is "level-pegged" step by step with Ezekiel (but concerning the second temple instead of the first), Revelation uses Gog and Magog as an allusion to describe the end of this current age (in which God is working behind the scenes as He did in Esther). Dispensationalists believe these passages speak of the same battle, even though the specifics are very different.
The idea of "dispensations" is not unbiblical, but the cycle of the various covenants must be taken as a progression. It is chiastic, but it is progressive, and the prophets always allude to previous cycles to explain what is coming - such as the wolf and lamb, the branch, etc (from Noah) to explain the restoration of the Land of Israel from beneath the flood of the nations.
Dispensationalists have a terrible time with the book of Hebrews. It's like looking at green through a red filter. It just comes up black.
The downside of dispensationalism is that is has no mind for types and symbols (at least not ones concerning Israel). The upside is that all the dispensationalists I have known have a very high regard for Scripture and Bible chronology.