Other than the obvious loss of information, I'd be interested in knowing what pitfalls come up that are specific to this case. To make things a little more concrete, take the case of a GPCR dopamine receptor. Supposedly dopamine (or one of a variety of drugs) interacts with this receptor in such a way that a different region changes conformation which in turn alters the conformation of a G-protein so that it binds GTP. This all seems to require very specific protein conformations and I can see how observing the average of many could be misleading.
Well, the main pitfall is what I already mentioned - if the conformations being averaged really are very different, this will decrease the effective resolution of the reconstruction, which will be very obvious even to an untrained eye. EM used to be notorious for producing vague blobs, in part because of the limitations of the technology (before they had direct electron detectors and had to use film), but also because the software tools (and users) weren't as good about picking out different conformations. And when the individual protein domains (often of known structure) resemble spheres in the reconstruction, it's difficult to tell that something isn't working. So it was indeed possible to generate a map that was a misleading average, and there are probably structures like that out there. But that's why everyone relied on crystallography for detailed structural information.
The good news is that at the resolution range people are using now, it should be possible to build individual structural components, but only if the particles are nearly homogeneous. So the ability to build (or dock) atomic models that clearly fit the map on the level of individual amino acids becomes a test for whether the averaging is justified.
The case you mentioned isn't really applicable, because the GPCR only assumes that conformation when bound to dopamine, and tends to work like a molecular switch. And of course if we did have a range of conformations being looked at, the reconstruction would resemble a soup can, without any atomic detail, which isn't really a publishable result. GPCRs are so small that it's currently better to use crystallography, but there are indeed structures of GPCRs in various static states at high resolution.
The remaining problems are that a) proteins aren't really static and b) the experimental methods for structural studies may induce non-physiological artifacts. I don't think (a) is that much of a problem because we have plenty of ways of studying protein dynamics and everyone is implicitly aware of this limitation anyway. The second problem is potentially worse: purification can sometimes have weird effects, crystallization packs molecules into a lattice that may not represent the native conformation, both crystallography and EM typically work at cryogenic temperatures which is known to change the structure in various ways (mostly but not always subtle), radiation damage can have side effects too. Much worse are the older "negative stain" EM structures where the proteins were covered with uranium or something similarly massive and sandwiched between thin sheets of carbon. Fortunately this is much less common now that cryo-EM has gotten so much better.
Ultimately the value of any model is determined by its ability to explain biochemical data and suggest new testable hypotheses. That's ultimately the most important way to validate their accuracy, and researchers ignore it at their peril.