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Gunzorro's advice is all good.
Looking at your crops, I think maybe your focus point in the third example is on the mask instead of the eye, which is a problem you also get all the time with glasses frames. Your AF picks up whatever shows the best contrast. If you know that is likely to happen, you can autofocus, and then give your lens a minute manual twist to the left—a little practice will help you gauge how much is needed.
The other two shots also show eyes in shadow, which lowers contrast and makes them tough focussing targets. Photographers who rely on natural light in dark venues have no choice but to become expert at judging particular spots that may provide good facial lighting, good contrast, and natural catch-lights for the eyes. Concentrate on shooting as much as you can in those places. General darkness is also general flatness; learn to see that and avoid.
Be alert to the possibility that artificial lighting environments sometimes produce light in colors that slightly confuse AF systems, which are optimized for some-color which you may not be getting. When I was doing stage photography I learned that my AF was almost always going to miss when they went to deep red stage lighting. Using more-than-minimum depth of field is an answer, but it is a better answer when you have a shorter lens to help out, especially when things get really dark and you can't stop down much.
I don't think long lenses are usually good choices for dark environments, even with IS, because of the shallow depth of field. And for the kind of shots you are showing, foot zoom works fine. When I was doing that kind of work, my favorite dark-venue lens was the Canon 35 L. With that lens you get focus-forgiving depth of field combined with edge-to-edge sharpness at about f/3.2. Excellent bokeh, too, in most situations where you are close enough to fill the frame with a person or two. And you are ready to go really wide when things get really dark. With the light you had, you could afford to close down even more, and still have plenty of shutter speed for that lens. Maybe have room to lower the ISO a bit on the shot of the couple. I think the 35L is a dark-venue sweet spot. And I was shooting everything using focus and re-compose. With the AF in the 5D III that lens ought to be a killer.
Most event pros who use zooms are also flash photographers. If you want to cut against that grain and use ambient light, I suggest fast primes, on the wide side. Let short focal length provide the depth of field and motion stopping capability you need at your limited shutter speeds. Wide lenses are also better story telling lenses in a crowded room. You have more composition options. It's a different kind of photography, and less reliable for delivering the goods on every shot. It can provide sensational images, but you had better get awfully good at it before you undertake to do something like a wedding that way.