The problem is that consciousness happens "now", but "now" has only a meaning in an inertial frame of reference, and simultaneity in physics depends on the chosen frame of reference.
To phrase it differently, you generally don't feel what you felt yesterday, or what you feel tomorrow. You only feel (or experience) what you are feeling at this very moment. But if one (mathematical) point in the brain is conscious, by the time it has communicated to another point in the brain, that "feeling" has been lost to time.
So either consciousness happens only at distinct (mathematical) points in the brain, or, somehow, consciousness can span a short non-zero time interval. You experience not just "now", but also briefly in the past and perhaps into the future.
This seems contradictory, so a better way of looking at it is needed.