Which substance may pass through a cell membrane by simple diffusion?
Depending upon the source you use, the certainty of the answers to this question are unclear. Some textbooks will plainly state that water and carbon dioxide may pass freely across the membrane, and that this is their normal means of transport. However the exact biomechanical explanations for this ability are often left unstated, except for the fact that these molecules are incredibly small compared to even a single phospholipid, therefore implying that they are able to simply fit through "cracks" in the membrane.
However, this seems to be at least partially contradicted by other considerations of empirical evidence as well as observations. The exterior of the cell membrane is polar, while the interior is nonpolar; this means that charged molecules like water will greatly "prefer" to stay out of the interior. Nonpolar molecules, on the other hand, need only pass the polar barrier. Another way of interpreting transport rules is whether the molecule is soluble in water or fat; fat-soluble particles have an easier time being transported. Water transport directly through the membrane has also been found to be an insufficient method to account for the actual rate of water flow.
The attached research article cites some of these concerns, and asks whether the membrane poses an obstacle to CO2 transport. The research found that CO2 was capable of moving through the membrane without the need for protein transporters, and therefore CO2 would be a good example of things which can directly diffuse.