I'd give it some more time before getting worried. It appears that your lens is at least capable of taking sharp pictures. For example the shot of the dear is sharp, as well the 'ear' of the woman you took a picture of is very sharp. Are you using a focus region or a selected focus point? The other shots could do with being a little sharper, the first image of the fence and flowers as well as the image of the bike should be sharper on that lens. I have a copy of the 24-70, it's razor sharp throughout on both full frame and crop.
Higher shutter speeds, practicing steady hands, taking multiple pictures of the same image, practice focusing. The advice above about using a tri-pod with a delayed 2 second shutter and shooting with various settings in live view is worth trying. I don't see anything that jumps out as a problem with your lens, so do a bunch of tests, get good at it before you start worrying. Also, just a basic note for you, if you are shooting wide open at 2.8 on a scene with objects at varying distances, only the objects in line with what you focused on (focal plane) are going to be in sharp focus, everything else will gradually recede out of focus, so you may want to pay attention to testing at higher f/numbers as well as faster shutter speeds. Also, I would compliment your composition, the framing choices in all of your shots is quite good.