EDIT: The attached photo is the most easily accessible example of the conduit used in the entire house. This shows the conduit attached to the garbage disposal with the previously mentioned 3/4 set screw connector. Not shown is the wire contained inside. However, the wire is just loose insulated conductors that have a fairly large amount of play and in some cases, slack where you can pull additional wire out of the conduit up to a point. It doesn't look to me like that would be possible with the conductors in an armored cable.
All of the outlets in our house test as being properly wired (i.e. include the presence of ground). The house is wired with 12ga THHN pulled through flexible metal conduit. However, ground conductors are not present anywhere. Thus, each jbox is grounded only by its connection to ground through the conduit.
My concern is, although there may be electrical continuity to ground via the flexible conduit, the electrical connection at each jbox must be rather poor since the conduit is physically connected only by a set screw. Said another way, I really have to question the ability of the conduit to carry any significant fault currents.
I suppose if all the circuits in the house were on GFCI breakers, a crappy ground wouldn't be much of a safety issue since the ground could certainly carry enough current for the breaker to detect the current mismatch and trip. Since that isn't the case, it seem to me that any path to ground needs to carry enough current to be able to trip a regular 20 amp breaker in a timely manner.
Are there any significant safety concerns with this method of grounding, and/or should I consider having ground conductors pulled or, I suppose, having the house rewired with new 12/2 (or 12/3 for the multi-wire branches)?

I am pretty sure it is flexible conduit. The conduit connects to jboxes with 3/4 EMT set screw connectors. There is also a lot of internal volume to the casing. Even running with 3 conductors (which look like thhn), it looks like you could fit a run of 14/2 through there with room to spare. I will need to look more carefully later to see if there is any bonding strip included, but I don't think there is.
– bobfandango Oct 06 '14 at 22:17