I think kenhung mentioned this in his comment but in my opinion, the fluid mosaic model can be looked at in three aspects:
1) protein channel
2) arrangement of phospholipids in the phospholipid bi-layer.
3) movement and flexibility of the plasma membrane.
The plasma membrane is made up primarily of phospholipids, forming the phospholipid bi-layer, and protein molecules forming the protein channel. Hence - its mosaic (sort of like pattern) When the plasma membrane moves, it moves in a lateral movement; that is, if the upper layer moves, the bottom layer also moves. This laterall movement is actually partially controlled by the presence of cholestrol in the plasma membrane, which reduces fluidity in moderate temperatures to retain the lateral movement of the membrane, or increase membrane fluidity in cold climates. Hence, its ability to move - fluid.
The semi-permeable membrane itself is actually also an asset that justifies its fluid-mosaic model; its ability to allow the movement of substances due to it being partially permeable.
Someone please fix up anything that is inaccurate, but I'm pretty sure the reasons about justify its description as a fluid-mosaic model.