Your lens is most likely fine. There are a couple of things that could be happening here.
Firstly, it's important to understand that phase-detect autofocus, the kind of AF you have in normal shooting (not live view) is optimized to get a decent focus lock quickly. It's not super precise, so with an f/1.2 lens you are going to have focus misses if you're taking shots at f/1.2, especially in anything less than ideal conditions with good light and a nice contrasty-edged target. The AF system has to "look" through the lens, so it's going to be even less accurate with a lens that is soft wide open. Zoomed-in live-view AF is going to be much slower, but more accurate.
Secondly, your lens body combination may need micro-focus adjustment. It's not uncommon for a fast lens like this to not be perfectly spot on. With slower lenses, the increased DoF usually has you covered. Not so at f/1.2. There are Youtube tutorials that show you how to do MFA, it's a slow, painstaking process that requires a lot of test shots in order to differentiate lack of precision from lack of accuracy. It's critical to understand the difference between precision and accuracy to take and interpret the measurements properly, Google it if you're unsure. MFA can only correct accuracy; i.e. a consistent tendency to front or back focus, it won't help with a lack of precision that is inherent with phase-detect AF and a fast lens. This is why you need to take a statistically-significant number of test shots when MFA'ing a fast prime.
Thirdly, hand movement. Even a slight sway or twitch between AF lock and shutter release can move the focus point. Tests have to be done on a tripod, as windpig outlined.
Fourthly, the center AF point is potentially larger and not perfectly aligned with the etching you see on the focus screen. If you're focusing on a tiny detail in complex 3-dimensional scene, the AF system might be focusing a little bit in any direction from where you think it is. Just something to keep in mind.