After breaking a water source the water doesn't go away and I've had to place blocks over each spot where the water remains in order to get it to go away. Occasionally the game acts like there is an extra water source where if I place a block in certain parts of the flow it seems to update some of it and more of it will clear away but it doesn't force all of it to go away.

I haven't played the game long enough to know if this happens to water sources that the player places but I've noticed it a lot when going through caves where the water behaving this way gets in the way of exploring the caves.

Even exiting the world and reloading it doesn't get rid of the water. 

Mobs and the player are affected by the water's existence and can swim in it too. Standing in it also causes the air bubbles to go down and you can drown in it as well.

This is on a singleplayer world.