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If I understand correctly, autofocus works with contrast detection or phase detection, and both of these systems are in the camera rather than the lens. Surely then, the camera just needs to control the focus motor until its detection system reports a peak focus value.
If that's the case, why do lenses have front/back focus problems, or exhibit even more complex focus issues that are a function of aperture or subject distance?
Contrast detection autofocus systems work in a closed feedback loop and so the lens shouldn't cause misfocus. However phase detection AF is not completely closed loop (it's also not fully open loop), several measurements are taken and the lens instructed to move a certain amount calculated to correct the observed phase disparity. The calculated phase difference and the required lens movement are sources of error, however you would expect this error to be noticed when the next measurement is taken. It appears that when only a small phase disparity is detected the lens is instructed to move to the final position and no further measurement is taken, and this is where focus errors arise.
It's worth pointing out that the way phase detect AF systems work is not all that well understood. Most of the literature describes to phase detect systems as being purely open loop (one measurement, no feedback), however people have devised experiments to prove that with most cameras this isn't actually the case (e.g. you wait for the lens to move and then block it with your hand, the camera will continue to try and focus and wont give you the confirm beep until you take your hand away, proving it's waiting for additional measurements).
It's unclear to me exactly why phase detect systems aren't purely closed loop either, as that would seem to put all the "my lens front focuses" issues to bed. If it were for speed reasons (i.e. the extra measurement delays the firing of the shutter in many cases when the lens is actually correctly focussed) that doesn't explain why there isn't a slower but more accurate AF setting for when speed isn't a priority.
Focus shift: another source of focus problems arise due to the fact that the camera focuses with the lens wide open, and then stops down to take the image. In lenses which suffer from pronounced uncorrected spherical aberration the plane of sharpest focus can shift when stopped down. A good example of such a lens is the Canon EF 50mm f/1.2L. The shift occurs between f/1.4 and f/3.2, from f/3.5 onwards the increased depth of field makes up for the focus shift. This problem is only really remedied by knowing about the problem and compensating or manual focusing whilst stopped down.
Sometimes the sensing system is tricked by the amount of infrared light in the scene. This caused backfocus issues with the Pentax system when used under incandescent lighting. They added the ability to tweak the system to modern cameras to allow for changes. It's my understanding that more recent versions of their cameras have fixed this problem.
The other parts can be caused by registration of lens to body variances. I've been lucky that my autofocus lenses seem to meet the midrange of their tolerances. I've heard of others that may have a body that when in combination of certain lenses produces a combination that is out of the range of acceptable use.
With contrast detection autofocus, the camera is working with data from the main imaging sensor, and in theory the results should be perfectly accurate, with no possibility of misalignment — as you describe. In the real world, the algorithm may give up too soon (in the interest of speed), or have other flaws. Or the part of the image you want to focus on may be confusing in some way (from an algorithmic point of view).
With phase detection autofocus, though, the autofocus sensors are measuring light which comes through the lens and then is diverted via the mirror. So, there's an additional optical path, and there's the possibility that the distance is simply slightly off. The phase detection itself may be perfectly accurate, but since you're not recording the final image from that exact plane, the actual result may be off.
One can have a similar problem with manual focus if the focusing screen isn't precisely positioned.
