You mention that it has issues with still subjects?
Puut the camera on a tripod and take images of a flat wall about 15 ft away with a 50mm focal length.
Thak 10 shots moving the focus to infinity before each shot. Make sure your shutter speed is at least 1/100 of a second, and set the aperture to wide open.
Variance in critical AF is normal, but 8 or 9 should have sharp focus.
That should show you that the focus is ok, or that it is bad. The worst thing is when its erratic and every other shot is off. That can be the camera or the lens, or a combination of the two.
Many of us went from a 8 or 10 mp camera to the 7D and started viewing images at 100%, and were appalled. It takes more care and twice the shutter speed to get the sharp image you are used to seeing at 100%. Once you get it down, then your images will be sharp, but its still a challange when you view them at 100%.
Now, just imagine those D800 users when they went from their 12mp D700 to the D800. They had to learn to be very careful, and even then, viewing at 100% can be frustrating. I was one of them, but I went from a 5D MK II and 7D to the D800. After a couple of thousand images, I got really tired of the long time it took to post process images and sold it, so I now have a 5D MK III.
Here is one of my first batch of images with the D800. It was a struggle!
100% crop ---Frustrating and Fuzzy!!
By the second event, things were better. Same camera and lens, more experienced photographer
100% crop Much better, but getting the apparent sharpness of a 30D at 100% requires ultra careful shooting, and thats not me!