Focus help

The two photos I've attached obviously have some focus problems. I took several action shots today and all of them have the same issue (dog out of focus). This is especially noticeable when I start cropping.

The first one the settings were as follows:
f 13; 1/400; Tv mode; ISO 400; AI Servo; Continous mode; Automatic Point Selection for AF.

The second one the settings were as follows:
f 5.6; 1/500; Tv mode; ISO 200; AI Servo; Continuous mode; Automatic Point Selection for AF.

Is it my skills (hopefully), limitations of my camera/lens (T2i/Tamron), etc.
Is there anything different on the settings I could have done to ensure better success on the shots (Manual selection-center point for the AF, faster shutter, etc.)?
Any advice is appreciated.
Thanks,
Randall

HOSTED PHOTO
please log in to view hosted photos in full size.

HOSTED PHOTO
please log in to view hosted photos in full size.

If the dog is running at you, I would think you might need a faster shutter speed as the dog is constantly leaving the focus zone?

First picture it looks like you used on camera flash?

Sure would help if you had included the EXIF data, but the first does look as if flash as used so the camera may have dropped to 1/200. It looks like motion blur to me.

The second looks like it is just missing, focusing behind the subject. Does the lens nail focus in stationary objects? One thing you might try is taking a burst of a few pics. Then choose the one where it nailed focus.

Sorry about the EXIF data, not sure how to include it (I use DPP).
No flash on the first.
I think it is fairly sharp on stationary objects:

HOSTED PHOTO
please log in to view hosted photos in full size.

Automatic point selection for AF - you should be selecting the AF point, not the camera.

#1 looks like vertical camera shake to me. Nothing is in focus and looking at some of the horizontal lines you can see vertical shifts. You were panning from up to down to follow the action and jerked a little too much perhaps. A faster shutter in this situation would help and it seems that you could easily have shot at 1/1000 or faster with all that available sunlight. Compare to #2 where there is no camera shake detectable and the focus looks pretty close but as mentioned perhaps a little in back of the dog.

use single point (center or off-center), NEVER let the camera make a choice of what YOU want it to focus on.

Make sure you are using servo mode too.

Thanks for all the replies.
That was one of the main things I was concerned about was the Auto Point Selection. I wasn't sure what the best one was to use for action shots.
Randall