1) There are currently two separate CORs for each contract. Should both CORs be present for inspections since we have a medical contractor inspecting a food contractor.
2) Can one COR be appointed to both contracts and represent both parties during the inspections, or could that be viewed as a conflict of interest?
This is a great question! The scenario you describe above is not uncommon at all; we normally refer to it as a “3rd Party Audit”. A scenario where the requiring organization does not have the technical expertise to conduct inspection on contractor provided goods and/or services and therefore must rely on a 3rd party to conduct the inspection. Sometimes another government agency is the 3rd Party and sometimes we must contract out that expertise (like the scenario you describe).
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One of the reasons we can contract out inspection is because “inspection” in-and-of-itself is not an inherently governmental function [reference FAR 7.503(d)(17)]. However, government “acceptance” is inherently governmental [reference 7.503(c)(12)(v) and 7.503(c)(17)]. Note: bold italics added for emphasis.
So, to address the title of your question; there is “NOT” any automatic ethic and/or legal concern with contractors inspecting other contractors, so long as the two contractors do not have any fiscal or financial or personal relationship with each other [See FAR Subparts: 3.5, 3.11, and 9.5]. If they do… that would be a problem; an “organizational conflict of interest” problem!
On to your specific questions…
1) There would be no problem having both CORs present for inspections, but it isn’t necessary. This assumes that both CORs know they are free to communicate with each other should issues arise about the veracity of what the contractor’s may be communicating to them.
2) There would also be nothing wrong with having the same individual be the COR on both contracts. This assumes the COR has no personal conflicts of interest (i.e. owns stock, spouse works for, etc.) with either of the contractors. It also assumes one COR can handle this workload.