Hi jpat1975,
On the specific question of 1 Corinthians 11:3-16 (the matter of gender differences and head coving/hair length), I have written extensively to show how a passage like that might responsibly be exegeted. You can find the article here:
http://www.thenarrowpath.com/ta_headcoverings.php
Briefly, "shame" refers to the cultural reaction and social opprobrium associated with certain gender-style norms in the Greek culture (i.e., that of Corinth). In verse 16, I believe that Paul disavows any adoption of such norms in his own culture. In fact, Paul had a Nazarite vow while he was in Corinth, which would have forbidden him to cut his hair until it was completed (Acts 18:18). "Long" is admittedly an entirely "relative" term with reference to hair, and is never defined. It was unnecessary, because the Corinthians knew what length of hair, in their culture, was normative for men. From surviving statues of Greek men, we might deduce that men wore closely-cropped hair—considerably shorter than many conservative American men wear their hair. But then, Paul was not writing about conformity to American culture, but Greek.
Since American culture commonly accepts without discomfort almost any length of hair on men or on women, we have no "instinct" (i.e., no "nature" teaching us—1 Cor.11:14) precisely what length hair must be in order to qualify as "long." When the Beatles became popular, in the 60s, they were noted for their scandalously "long" hair. Today, it is neither scandalous, nor surprising, to see hair on respectable businessmen, pastors, doctors, lawyers (even presidential candidates!), and other professional people that is longer than the Beatles originally wore their hair—and it is not even regarded as "long" hair today. If Paul had written to us with similar concerns, he would have had to define the length of hair that he was objecting to—but not in ancient Greece, where men's hair styles were fairly standardized.
Paul, in the passage, does not actually express concerns about the Corinthian men's violation of local "custom" (v.16) by wearing long hair, because, in all likelihood, men were not deviating from the cultural norm. He is writing because there were women defecting from the cultural norm, and Paul felt that this practice would send inappropriate signals to observers (as we might say a modern Christian woman in the attire of a prostitute would be sending inappropriate messages). We may not realize how cultural some of these matters are. An American woman walking about in public bare-chested would definitely be thought to be sending a message that a Waorani woman in Ecuador would not be sending by the same behavior. The problem of Christians sending the public inappropriate messages, by a controversial expression of their Christian liberty, is, in fact, the burden of Paul's instructions in the preceding section (chapters 8-10).
But your larger question is, "How do we decide whether passages of this sort are universally applicable, or simply cultural accommodation? The best answer is that each passage must be taken case-by-case. In most cases, making the following inquiries about a passage would seem helpful:
1) Does the duty suggested embody some actual moral or spiritual principle, or is it related only to cultural norms (e.g., "Does the master thank his servant because he did the things command? I think not"—Luke 17:9)?
2) Does the same, or a similar, concern find confirmation elsewhere in scripture? (e.g., Are we to "baptize for the dead" if we find a sole reference vaguely alluded to without explanation?)
3) What is the author's core concern? Can the concern be accommodated with some flexibility in detail, or not? (e.g., when Paul asks that we greet with a holy kiss, would a warm hug or handshake suffice to accommodate his actual concern?)
4) Do the instructions contradict other instructions found in scripture (e.g., If it is universally shameful for a man to have long hair or cover his head while praying, then why did God command Nazarites, like Samson, to never cut their hair? And why were priests ordered to wear a turban while conducting their worship duties?)
5) Does the command begin and end with concerns that are merely "externalistic," having nothing to do with the state of the heart (e.g., Paul's flexibility in abstaining from "unclean" foods when with Jews—1 Cor.9:19-20—even though he was aware that "Not what goes into the mouth defiles a man; but what comes out of the mouth"—Matt.15:11)." Observing the general principle that "man looks at the outward appearance, but the Lord looks at the heart"—1 Sam.16:7—will go a long way toward distinguishing between universal and transient behavioral requirements.
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