The term ‘materialism’ comes from philosophy, and denotes the belief that matter is the fundamental reality; it is also associated with Marxist cultural theory, from which materialist criticism derives many of its concepts. ("Materialist Criticism." Oxford Encyclopedia of Theatre and Performance)
Materialist criticism grows out of the Hegelian dialectic and out of Marxism. Dialectical process opposes an idea, a thesis, to its opposite, its antithesis, and develops a synthesis that replaces both thesis and antithesis. "Synthesis" in Hegelian terms is slightly different from the commonplace idea of synthesis, which is that separate parts are brought together to form a whole. In Hegelian dialectical argument, the opposing forces (the thesis and antithesis) are reconciled: reconciliation allows for results or resolutions to opposition that are different from the opposing parts. An example might be taken from the French Revolution during which the thesis and antithesis of monarchy attacked by revolution (thesis) and Revolution displaced by terror (antithesis) were reconciled in the synthesis of a constitutional democracy of free citizens, a resolution not contained within either thesis or antithesis.
"Discoherence" in materialist criticism might be said to be the presence of opposing opposites, of thesis and antithesis, in a theatrical production (materialist criticism is used for theater productions and examines both the Marxist framework--superstructure, ideology, etc--and the socio-cultural elements around the present-time production, which mark it as distinct from the original-time productions). Discoherence is defined by Jonathan Dollimore as "incongruity verging on contradiction" and is informed by the Hegelian dialectic (opposites reconciled).
In Hamlet one instance of discoherence might be identified as the murdered Denmark's insistent request for vengeance delivered by Hamlet's hand. In terms of contradiction, the King's demanding adherence to pre-Christian tribal rituals of vengeance killings contradicts the then present-day Protestant Christian State of Denmark epitomized by Hamlet's education at Wittenberg, the home of the Wittenberg University where Martin Luther taught against the doctrines, such as that of indulgences, of the Catholic Church. In terms of dialectic, the thesis might be familial tribal demands against the antithesis of mercy and longsuffering as religious dictum, which are reconciled in synthesis by multiple murders. This would illustrate discoherence in Hamlet.
In King Lear, Lear and Cordelia might represent discoherence through a classic sort of Marxist dialectical thesis and antithesis. In this scenario, Lear would represent the oppressive State while Cordelia would represent the oppressed proletariat. The thesis and antithesis here are reconciled in the synthesis by anarchy wherein Lear is unseated and Cordelia is conquered at the feet of the equally conquered Lear, whose authority is assumed by another. In terms of "incongruity verging on contradiction," Lear's autocratic demands force Cordelia to bespeak herself as disloyal when she is in truth the only loyal one: we have State demands (laws) resulting in proletariat disaffection. This would illustrate discoherence in King Lear.
Nothing will come of nothing: speak again.
Unhappy that I am, ...
... I love your majesty
According to my bond; nor more nor less.