Hi Rich.

I think the answer is going to depend on a few things.   

Governing welding code, business accreditations, internal quality manual, & contract requirements all might come into play.

Some codes demand via WPS for the manufacturer and specific electrode brand name shall be included, and others do not.

One example would be AISC 360 Chapter N requirements.   Table N5.4-1 (Inspection Tasks Prior to Welding) specifies that manufactures certifications for consumables shall be available.

Another example is AWS D.18 seismic supplement, which specifies special "Product Data Sheets" for consumables used for Demand Critical Welds that must have heat envelop testing.

To add to Lawrence's list: obtain paperwork showing purity and dew points of shielding gasses, watch/check for fork punctures for pallets of hermetically sealed containers for SMAW low hydrogen electrodes, torn boxes or broken sealed rolls of FCAW wires that have seismic quality (atmospheric exposure limits) requirements....I'm sure there are many more that escapes my memory at the moment.