Seems to me the most useful measurement of sea level is the diameter through the center of the earth to the corresponding point at the other side of the earth. You would take those measurements at many locations and times, and average that distance. The change would be the difference in that distance from the last measurements.
That sounds nearly impossible to me, so I don't know what the method used today is, and what the drawbacks are. Simply measuring the distance to sea from some land point seems susceptible to much inaccuracy. Is the land abducting, or subducting? As land submerges, the water creates buoyant forces, and other complications. Same sorts of measurement errors SA brings up with regard to global surface temperature.
More measurements should provide increasing confidence and narrow the margin of error though.
All the water on earth is an 860 mile diameter sphere.
Maybe we just need to trench the Mariana trench a bit more?