Hi Ardy,
There are always trade-offs mate.
Underwater is a dynamic environment and everything is constantly moving, you, the camera, the subject and the water. . .always moving!
You have to have the camera set for a single focus point otherwise the lens will be chasing everything that moves in its 'vision'.
Pushing the shutter button will initiate the focus sequence as per normal and as long as the subject remains fairly still the lens will lock on, but it is harder to hold a point of focus on the eyes, as such. The camera doesn't know that you want to focus on the eye and will not hold focus on the eye just for you, what ever is inside the focus square is what it will focus on AND if you trip the shutter it will fire NO MATTER WHAT.
A BIG downside to all this focus activity is, of course, battery life. It will suffer!
If your camera is having trouble focusing underwater, I would suggest a good focus light. I know that every time that I turn my focus light on, the camera snaps onto focus instantly. I have also noticed that my EPL-2 focuses quicker when I have the red filter on also. I'm thinking that it might have something to do with the focus contrast system being used? i know that if I just have the bright white light that sometimes my EPL-2 struggles a bit but put on the red filter and it snaps to attention. . . .
These are just my experiences and other opinions may vary. . .

Bruce
Hi Bruce - I have had my set up for 3 years and another digital camera for 6 years and have never heard this and never used AF-C. This is a very useful piece of information.
Any downsides to AF-C? Of course if you want to set the focus with shutter realease and then move camera to focus I guess it will refocus - is this correct? if not this can be useful.
regards