Andrew is wondering whether you activate autofocus (without the remote on) with a half press of the shutter or via the AE-L / AF-L botton on the back of the camera.

As that seems not to be the case, what autofocus mode are you in? AF-A, AF-S or AF-C? I think that if you are in AF-C mode you will have the problem that you are describing (because the camera is set to take a shot even if the scene is not in focus) whereas with the other two, focus must be locked before you can take a shot.