What I expected to happen was...
Mobs act the same way they do on land while in the water, besides jumping to breath.

What actually happened was...
Seemingly randomly, mobs will get "stuck" in deeper water and will not move nor will they watch or follow the player. After watching 2 full day night cycles, I saw a 3 creepers float from land into deepish water then stop responding. When I got close enough to them they blew me up. I also saw two other creepers going from land to water and back to land without problems. I came up to a skeleton that was "stuck" in the water and it shot at me but remained stationary. What I found very odd was that peaceful mobs that are "stuck" can be pushed closer to shore and once they are about 3 meters away from a solid block they "remember" how to swim forwards and begin moving on their own until they get "stuck" again.

Steps to Reproduce
1 Wait a full day/night cycle and watch both peaceful and hostile mobs that are in deep water.
2 Push a peaceful mob that is "stuck" in the water closer to land but not on land
3 Get near enough to a creeper or skeleton that is "stuck" so that they attack you.