Some key points:

Focus points are larger than the LED that lights up. As a result, the camera will pick anything within the area, usually the with the most contrast (often what is closest yet not too far on the edge of the AF sensor).

Depth of field is larger with a shorter focal length, and of course with a smaller aperture. What this means is that the AF sensor will say that the area is in focus even though it is on the edge of the field in focus and not centered.

Some other interesting facts about focusing:

Some lenses, due to spherical aberration, change their plane focus when stopped down from wide open. This mostly affects fast lenses.

Many AF sensors are only accurate to around f4 or f5.6. This means it will stop when an object is within the acceptable focus for a depth of field as if the lens was at f4 or f5.6.

To really check for accurate focus, you should use a focus chart with only one spot of contrast, so you can be sure of where you are focusing. I like to use this, page 18.

An even better test is the moire interference test.

Lastly, many lenses perform quite different at close focus distances (usually much worse, with softness, haloing, and other aberrations that may not be present at all otherwise). Try to take some pictures of objects further away and compare it to full-sized samples from the same model.