While using rivers to divide states may seem conceptually simple, the natural tendency of river courses to change over time has caused complications. If you look carefully at maps and legal history, there are numerous territorial oddities and disputes that have arisen over the years.
For instance, a series of earthquakes in 1811-12 shifted the course of the Mississippi River in a way that stranded two Tennessee towns—Corona and Reverie—west of the river in what seems like it should be Arkansas. Upstream, the same earthquake, and a lack of precision by early surveyors, left a bit of land known as the Kentucky Bend completely surrounded by parts of Missouri and Tennessee. Meanwhile, Kentucky and Indiana have engaged in a protracted debate about which state owned a piece of land near Evansville that connects to Indiana if the river is low but becomes an island if water is high.