Hi Roger,
First thing that comes to mind is that the AF on the Nikon D3 is superb... as good or better than anything I've ever used... so it's likely to be your settings (or technique) and not the camera. Second, if you switch around between systems, like you and I do, it's very easy to forget how you want the system set up. The interactions between active AF points and all that other stuff is confusing as heck. Let me pass along my settings and you can see if they work for you. You may recall though, that I am NOT a half-press of the shutter to focus guy. I'm one of those thumb on the AF-ON button to focus guys. To my way of thinking this avoids the potential of inadvertently refocusing when you do your usual focus and recompose... but that's a conversation for another day. First off, on the front of my camera my focus mode selector is set to C... and it stays there. Don't care whether the subject is stationary or moving... this is working just fine so I see no reason to change it. Second, My AF-Area Mode selector (the one to the right of the LCD screen) is set to Dynamic (the middle setting). This ties into the number of focus points you select in the menu but just forget about that for now, it's confusing as hell. Next, let's go into the Custom Setting Menu and select Autofocus. The first choice in that sub-menu (a1) is set to Release, so is the second (a2). For a3 I have selected 21 points as my Dynamic AF area, a4 is set to Long, a5 is set to OFF, a6 is set to ON, a7 is set to ON, a8 is selected to 51 points, a9 is set to ON (this is the setting that changes the focus method to thumbing the AF-ON button for focus), a10 is set to Same as AF-ON. These settings are different than Stuart's but the fact that neither of us has any focus issues seems to me to be a tribute to the camera. I don't know if Stuart's comment about holding the shutter depressed has hit the mark, but it's one of the reasons I use the AF-ON button to focus. Let us know how you make out...