Diagnosing building failure is a task that, like diagnosing medical problems, must be performed in person. Having said that, a few basics of earthquake damage from the current news in Christchurch follow.
Some good photos from the Sydney Morning Herald. The cathedral tower collapse (sec0nd picture down) is what happens to unreinforced masonry in quakes: brittle failure which leads to collapse. The tower was most vulnerable because it was tall, slender, and relatively heavy.
The building that has collapsed except its front facade (3rd down, above the thumbnail gallery) appears to have had floor beams supported on an unreinforced brick side wall.
The picture on this page is disturbing, as this is a modern building pancaked from a relatively small (less than full design load) quake. The type of failure of the concrete columns and walls suggests that they were not reinforced sufficiently for ductility, which is the basis of modern design.
Interestingly, NZ has has earthquake codes almost as long as the US: we got them right after after the 1933 Long Beach quake, NZ did after quakes in 1929 and 1935. Buildings built before seismic design can be retrofitted but are almost never as resilient as those designed and built for seismic loading; since our knowledge about how to build for earthquakes increases with each major quake studied, each generation of buildings should be less vulnerable than the one before.
This is also the second quake to hit this area recently. Damage to brittle materials is cumulative, so even though the first quake was bigger, it is not surprising that there is severe damage now.