Localized extraction testing is one option.

Foresite (an analytical laboratory in Indiana) provides both bulk and localized extraction testing. Using one of their localized extraction testers (C3), one may extract contamination from a very small area (0.1 in2).

The extracted sample can then be subjected to ion chromatography for identification. One you identify the specific contamination, you will likely know its source.

Unless you have access to SEM with EDAX or some other chemical analysis equipment, then you need to break down the problem to understand where this substance is coming from.

Does the substance have color? Blue green could indicate copper from plating solutions.

Does the substance melt when heat is applied? This could indicate the glue layer under the pad could be melting and oozing out.

If you send the board through the SMT soldering step with out the component do you still see the problem? This can help narrow the focus of the investigation.

If you have opens, then you have a bad joint or a break in the lead to the pad. Have you tried to X-Ray the board to see if you have a break in the track after soldering? The substance may only be a secondary problem and not the cause of the opens.

Without a visual inspection of your printing processes or knowledge as to how you are cleaning your stencils it is difficult to pin point and correctly answer the problem. What you are describing sounds very much like an issue I have encountered in the past, and occurs when fiber debris is left on the stencil and transferred to the paste.

Stencil aperture hole-walls are sharp and can act like a shredder if the stencil surface is being wiped with a non-approved stencil wipe. Paper towels, shop towels etc. will deposit shredded fiber into the aperture walls that will be transferred to the paste and subsequently onto the board.

If this sounds like your practice, avoid further issues by using approved stencil wipes and utilize practices such as blowing off the stencil with compressed air to remove any remaining debris. Remember anything remaining on the stencil will transfer to the paste.

If this is indeed the cause of foreign substances appearing around the PCB pad it will become immediately apparent, once you have made these simple changes.