Well, if you want to talk about the mouth of a river or creek in terms of one that flows into saltwater, boy I have got a curveball to throw your way!

When the tide comes in the river gets "backed up" right? Nope! Since freshwater is denser than saltwater the river flows under the saltwater. What you get is essentially a separation of the two bodies of water as a result of salinity differences. So the river is not really "backed up" it just isn't visible since the saltwater is on top of it. This oceanographical event is referred to as the saltwedge.

Imagine you were looking at the river from the side, the tidewater section of river could be best represented by a simple diagram in the form of a rectangle. The river flows to toward the left side of the rectangle while the saltwater flows toward the right side. Based on the previously given info from the saltwedge explanation, we can draw a diagonal line from the lower left corner to the upper right corner to indicate the halocline(salinity boundary for water) and pycnocline(density boundary water). What you now see is two triangles within a rectangle, the triangle on top would represent the saltwater and the one on the bottom would represent the freshwater.

Now that you people know what a saltwedge is like, we can proceed to define the river mouth. We know the river flows into the ocean when not influenced by an incoming tide. When viewed from above, you would see the river form a fan-shaped delta under the saltwater where it flows into the ocean. Despite the fact that we are some distance out in the ocean, the seafloor is influenced by the river as evidenced by the delta. You would determine where the river "ends" by lowering a probe to the bottom from a floating device and measuring the salinity. You would keep moving offshore until your meter reading stops changing. This number is your normal ocean salinity. At this point there is no longer a freshwater influence.

Based on the above statements, I conclude that river mouth is determined to be the point at which salinity change ceases and an equilbrium is reached. Basically despite no longer being bounded by land on two sides, the river continues when it enters the ocean and the mouth is where it stops.

By the way, this is just my opinion and it will likely never be accepted by the WDFW for regulation purposes.