Andy raised a great question on the Focusing | Center and Recompose the shot or Use available focus points or that I wanted to share with you here, in case you do not read the comments on this blog.
When I am following my 16 month old around, I keep the AF on continuous mode (C) and try to focus on one of her eyes. What I have found is that, when shooting in the range of f1.6-f/2.0 with my 50mm; the second eye goes a bit of out focus.
First off, kudos on your upgrade from the Nikon D40x to the Nikon D700! Excellent camera choice. Secondly, another kudos for braving to chase around your 16 month old with your camera! LOL… I know all too well what a challenge this is.
My suggestion: Using the continuous focus setting is the correct choice when your subject is moving toward you. For the out of focus eye, try shooting with a larger Depth of Field (smaller aperture) such as f/3.2-f4.0. Turn your ISO setting up a notch or two if you need too (D700 performs amazingly well at High ISO settings). When subjects are moving, it is going to be very challenging to get them sharp at 1.6-2.0, especially both eyes. If your subject is standing still and both eyes are on the same focal plane, you may get them both tack sharp… maybe. :-).
**UPDATE** Leann Marie brought to my attention that it would be kind of weird to chase around your “16 yr. old” with your camera. HAHAHA! This comment brought me to laughing hysterical. I have updated the text to 16 month old, as it should be. Thanks Leeann! You made my day!!! Nothing better than started off the day laughing your but off. Have a great day!