The problem of the unity of consciousness for materialists is what makes activity in different areas of the physical mind come together into a single phenomenally unified state rather than multiple disconnected phenomenal states. If my auditory center active in the perception of a middle C and my visual center is active in the perception of red, what makes it be the case that there is a single entity that both hears a middle C and sees red?
We can imagine a solution to this problem in a computer. Let’s say that one part of the computer has and representation of red in one part (of the right sort for consciousness) and a representation of middle C in another part. We could unify the two by means of a periodic synchronizing clock signal sent to all the parts of the computer. And we could then say that what it is for the computer to perceive red and middle C at the same time is for an electrical signal originating in the same tick of the clock to reach a part that is representing red (in the way needed for consciousness) and to reach a part that is representing middle C.
On this view, there is no separate consciousness of red (say), because the conscious state is constituted not just by the representation of red (say) in the computer’s “visual system”, but by everything that is reached by the signals emanating from the clock tick. And that includes the representation of middle C in the “auditory system”.
The unification of consciousness, then, would be the product of the synchronization system, which of course could be more complex than just a clock signal.
This line of thought shows that in principle the problem of the unity of consciousness is soluble for materialists if the problem of consciousness is (which I doubt). This will, of course, only be a Pyrrhic victory if it turns out that no similar pervasive synchronization system is found in the brain. The neuroscience literature talks of synchronization in the brain. Whether that synchronization is sufficient for solving the unity problem may be an empirical question.
The above line of thought also strongly suggests that if materialism is true, then our internal phenomenal timeline is not the same as objective physical time, but rather is constructed out of the synchronization processes. It need not be the case for this that the representation of red and the representation of middle C happen at the same physical time. A part further from the clock will receive the synchronizing signal later than a part closer to the clock, and so the synchronization process may make two events that are not simultaneous in physical time be simultaneous in computer time. I suspect that a similar divide between mental time and physical time is true even if dualism is (as I think) true, but for other reasons.