In the first photo, it appears to be in-focus but the shutter speed is 1/80 and it looks like there's a little motion blur in your son's face.
In the second photo, which I'm guessing may be part of a continuous sequence, the focus point seems to still be behind your son as he moves down the stairs. If you shoot a continuous sequence with the subject moving towards or away from the camera, you have to be in AF-C mode to maintain focus. AF-A should do this automatically but I haven't found it to be reliable. Also, the camera may just have been choosing the wrong focus point if you still have it in auto-area focus mode.
In the last photo, it's clearly focusing on the background. The default settings should have handled this case, as it will usually try to focus on the nearest foreground object. If you haven't tried it yet, switch to single (center) point AF so you know exactly where the focus point is. It means you have to be a little more accurate in framing your shot to ensure the subject is somewhere in the center of the frame, or focus and recompose.
I was initially disappointed with the number of photos I got that had motion blur or focus issues, and it really does seem to me that full-auto settings are not adequate for many situations. It's unfortunate, but I think you have to know at least a little about the various shooting modes to get the most out of the camera.
90% of the time I'm on center-point focus, single-shot AF (AF-S), and continous shooting mode. Center-point focus ensures I always know where the focus point is. AF-S ensures that the subject focus is always locked before it lets me take a shot. If the subject is moving towards/away from the camera at any significant rate of speed, then AF-C is needed, but AF-S works well in all other cases. I leave it in continuous shooting mode even though I generally only take 1 shot (which requires a very quick shutter press and release!). When I do want to take a burst sequence, it simply takes too long to dig in to the menu to change to continuous shooting mode, so I leave the setting enabled at the risk of taking 2 or 3 shots accidentally, which may waste some storage space but also gives you 2 or 3 shots to choose from.
To ensure high shutter speeds, you can shoot in S mode but that runs the risk of underexposing if you select a shutter speed that is too high for the available light. I generally shoot in A mode with the aperature as small as possible, and leave auto-ISO enabled in good light. Indoors, or in dim lighting outdoors, I'll manually set ISO to 1600 to ensure a reasonable shutter speed, but there's no guarantees - if the light level drops too low, a well-exposed shot is going to require a slower shutter speed and there's not much that can be done other than using a flash or waiting for one of Nikon's F/1.2 or F/1.4 lenses, which I'm very much looking forward to.
