Phospholipid movement in cell membranes
There must be charge considerations in the movement of molecules in the lipid membrane. There is also a consideration that some species of phospholipids will migrate to portions of the membrane with sharper or smoother curvature. 

Waves of electrical potential can propagate along a lipid bilayer as well, which is very important to nerve axons and extended structures like that.  

In general though the membrane is held together by vanDerWaals forces like other non-polar solvents.  As such, the movements of lipids and proteins and other amphipathic molecules in the membrane are still largely Brownian (random) in the 2D surface of the membrane.