What are the main differences between designing a pipeline for water, oil and gas?

Other than the temperature of operation and viscous forces, I would say that pressure is quite critical. The pressure for pipes carrying gases and fresh water is usually higher inside (though there are several instances for gravity flow). For those carrying waste water, the pipeline system is almost never pressurized. The magnitude of pressure leads to different directions of hoop stress in the piping material. The direction of hoop stress in turn determines the type of materials that can be used for piping. This is easily seen in daily life- pipes for incoming fresh water have to be metallic as they need to have good tensile strength. The pipes for the outgoing waste water are usually made of concrete as they experience compressive stresses only.

Temperature and pressure of the fluids to be carried. Also the elevation at which these will be carried, so the overburden pressure on the pipe will also be a major factor. Further, water pipes design failure won't lead to casualties but in the cases of oil & gas can be severe. The type of soil where these will be laid, will also be a major factor.

I'd say the process of design is very similar for all three. You consider: fluid temperature range; ambient temperature range; fluid pressure (departure and arrival); ambient pressure (for subsea lines, for example); rheology; density; contaminants (may determine corrosion, erosion or leak prevention integrity); pipeline distance; flow rate range; capex relative to opex (do you want to spend money upfront on a large, low pressure drop pipeline or spend more on powering pumps/compressors throughout operation); security and required reliability of the pipeline; company and industry standards; local and international legislation...the list goes on. The final design is different because the above considerations are often very different for oil, gas and water.