Does Earth's rotation cause sea levels to increase from east to west?
I ask as in Bill Bryson's book 'A Short History of Nearly Everything' on p.334 ch.18, he says

The Pacific is about a foot and a half [~46cm] higher along its western edge - a consequence of the centrifugal force created by the Earth's spin.


Bryson is right in the sense that in places there is a difference in height between the eastern Pacific and western Atlantic, at least in some places. He is however wrong about the magnitude of that height difference and wrong about the cause. From the Permanent Service for Mean Sea Level,

Sea level is about 20 cm higher on the Pacific side [of the Panama Canal] than the Atlantic due to the water being less dense on the Pacific side, on average, and due to the prevailing weather and ocean conditions. Such sea level differences are common across many short sections of land dividing ocean basins.
The 20 cm difference is determined by geodetic levelling from one side to the other. This levelling follows a 'level' surface which will be parallel to the geoid (see FAQ #1). The 20 cm difference at Panama is not unique. There are similar 'jumps' elsewhere e.g. Skagerrak, Indonesian straits.
If the canal was open sea and did not contain locks, i.e. if somehow a deep open cutting had been made rather than the canal system over the mountains, then there would be a current flowing from the Pacific to the Atlantic. An analogy, though imperfect because there are many other factors, is a comparison between Panama and the Drake Passage off the south tip of Chile, which has a west-east flow. (The flow in the Drake Passage is primarily wind-driven, but Pacific-Atlantic density must play some role.)