Great responses, all of 'em. So there is no question that under the parging, the concrete block closest to the crown is in rough shape, due primarily to exposure to the elements as the crown itself is badly deteriorated and the parging is flaking off. The freeze and thaw cycles in my area, where avg. snowfall = 10 ft., begin this time of year and continue until spring. One of the most highly regarded masons in town, who is done working outdoors for the season, has agreed to swing by "real soon" to take a look and give me some recommendations.
To recap (pardon the pun), the chimney consists of 2 flues, running parallel. One vents an oil furnace, purchased only months ago and located in the cellar. In the cellar, the furnace vents horizontally (via metal duct with an draft inducer) for a 10' run prior to making the 90 degree turn up the chimney. The furnace guy told me that the furnace is so efficient that much what goes up the chimney is water vapor. Very little heat makes it up the chimney. If true, this works in my favor to reduce chance of fire in the event that the liner is cracked, agree? A clay liner exits the chimney cap at the terminal end of this flue and rekees4300 made a good observation noting cracks in this liner. Does the clay liner run the entire length of the chimney (rhetorical?). If yes, how far down do the cracks extend? I think it's safe to say that it is impossible to know without getting a camera in there. Upon closer inspection, the cracks (there are two) are hairline (no gaps exists). While they may be hairline at the terminal end, there is no guarantee that larger cracks don't exist at some point beneath. Finally as was mentioned earlier, the only way to correctly ascertain the condition of the concrete blocks, within which the clay pipe and the metal pipe (see below) both run, is by removing the amateurish, unsightly parge coat.
The other flue vents a wood stove located on the first floor of the two story home. The stove is vented directly into a triple wall metal pipe, constructed of a stainless steel inner wall, an aluminized steel center wall, and a galvanized steel outer wall (reading directly from the paperwork left me by the previous homeowner). The metal pipe runs inside a clay liner which, like the furnace clay liner running parallel to it, runs up through the concrete blocks stacked above the brickwork. There may or may not be insulation between the metal triple-wall pipe and the clay. The pipe is professionally cleaned annually. I burn about 5 face cord a season and the sweep always commends me on burning wood that is well seasoned. He can tell because his work yields a limited amount of dust only, not creosote wafers or chunks.
To summarize, I think it's impossible to tell with complete certainty, the condition of both the concrete block or clay liner running within, beyond what is exposed. The critical nature of the components require me to err on the side of caution, however, and assume the worst. I've already slapped some quick setting cement in the cracks as recommended by tcreeley and others (see photo, not suitable for those with weak stomachs) and will get up there and revisit closely over the winter when there are mild breaks in temperature, if any. I'm going to find someone with a chimney camera soon and get a look inside both the clay and metal liners. In the spring, the amateurish parging will come down and I will probably have it rebuilt. I'm looking forward to it. I will sleep better at night.