The question (What Exactly Constitutes Dhikr?) I asked originally referred to the practice of taking some time out from your worldly distractions, sitting down in some quiet place and doing nothing else but stating sentences that glorify and praise Allah.
I myself have done this many times, and have seen others do it too, so I know the practice is common. In fact in a mosque near to where I live, a group of people get together every sunday evening (because they're usually free on sundays) in the mosque, dim the lights, close the doors, and do nothing but Dhikr for an hour or two.
In the course of continuous Dhiker of this sort, it becomes difficult to force one's attention constantly to the meaning of what is being said. Being human, the mind wanders off.
What I was originally asking was that if the mind wanders in this kind of Dhiker, will that Dhiker still be rewarded, as it's utterance is mostly a mechanical act? Does such mechanical repetitions have any good effects spiritually or is the person just wasting his time?
Some people take this habit really far and do continous Dhiker (and here by Dhiker, I mean the utterance of statements glorifying and praising Allah) even when it's obvious that they're minds cannot be into it. Such people usually carry a tasbeeh around with them all the time and mechanically move the beads around. I tend to think that this is not the kind of Dhiker that is required of us.
Islam has established certain norms and practices of worship. It does not restrict us doing Dhiker as much as we can but the kind of practice you referred to tends to form a new worship ritual which is strictly prohibited. We can not add anything to the prescribed forms of worship. It would be an innovation in the content of religion. Therefore you should avoid participating in such kind of gatherings. It would be better to portion out sometime from your routine and ponder over the blessings of your Lord upon you. The best form of doing Dhikr is prayer. Besides offering five daily prayer you can offer supererogatory prayer (nafal) for the purpose of remembering God.