In most cases, sulfides can be easily and reliably detected visually with a binocular microscope, or a hand lens. A local geologist or mineralogist could show you what to look for.
Be careful to collect a representative sample of each batch of aggregate that you inspect. You'll have to examine many grains of aggregate (at least a couple of hundred) to confidently detect small traces of sulfides, but that should not take long once you know what you are looking for. The aggregate producer should also be able to tell you if there is a history of such problems.
Section 13 of ASTM C 294, "Standard Descriptive Nomenclature for Constituents of Concrete Aggregates," discusses the different sulfides of iron. It says immersing samples in a calcium hydroxide solution, then exposing them to air will produce a brown coating in a matter of minutes if a reactive form of iron sulfide is present.
ASTM C 691, "Standard Test Method for Iron Staining Materials in Lightweight Concrete Aggregates," is a more rigorous test. It provides sampling and testing methodology, illustrations for use in visually evaluating staining of the filter paper, and specific concentrations of hydrochloric acid and ammonium hydroxide to use in chemical analysis.
It may be difficult to find a clean source if the problem is common in your area. Cleaning the building is relatively straightforward. Drill out the popped particle and remove the stain that runs down. However, that can get rather expensive if the stains are closely spaced.
This question is from the Aggregate Research Industries Web site, www.aggregateresearch.com. Tom Klemens provided additional input.