Inadmissible evidence in arguments?

In courts of law there are all sorts of rules (and arguments) about what sort of evidence is admissible. In philosophy and theology, different communities seem to have various expectations about "rules of engagement" for an argument to be valid.

So, here is an issue that I find increasingly troubling in discussions at the interface of science and theology. When and how is it appropriate to invoke technical scientific concepts and language in the course of the argument? 
Specifically, I mean discussing specific topics such as protein folding, the Higgs boson, probability in quantum mechanics, non-equilibrium thermodynamics, climate, neutron stars, genetics, chaos theory, carbon dating, ...

Here is my first pass at an answer. Two key ingredients are necessary for inclusion of technical concepts to be valid and helpful.

1. The speaker or writer must have a knowledge and understanding of the topic at the technical level. e.g., the actual mathematical equations of chaos theory. To me, reading a popular book on the subject is not sufficient.
[Perhaps, this might be softened to that they should have checked their argument with an expert who agrees that they are invoking the scientific concepts in an appropriate manner].

2. Some significant fraction of the audience should have enough relevant knowledge that the scientific concepts actually mean something  to them (rather than just being "buzz words"). Furthermore, do they really have enough expertise to actually evaluate the merits of the argument?

My experience is that these criteria are often not met. No camp seems to have a monopoly on this problem. It occurs, regardless of whether the speaker is a religious conservative attacking science or a liberal theologian trying to use science to promote their perspective. It seems just too easy to "wow" a sympathetic audience with technical "mumbo jumbo".