Hi Jim,
I’m not sure that the absence of the “good and necessary consequence” language in the Second London Confession is “all-important.” The men who wrote/edited the Second London Confession certainly seem to have employed the principle elsewhere in their theological writings. Anyhow, you might look at the responses by Richard Barcellos and Brandon Adams to CTC episode 234 (http://reformedforum.wpengine.com/podcasts/ctc234/).

Richard, I think that they all-important difference is the excision of “good and necessary consequence” in the 1689. Every other difference seems to flow from that. Is that fair?

The claim that the bar of membership should be set as low as mere “credible profession of the gospel,” should be questioned more seriously in contemporary Reformed and Presbyterian circles.
Even in those communions that hold to confessional membership and close communion, a difference between the affirmation required of members and the knowledge and ability to teach required of officers is maintained. For those interested in the argument for confessional membership and close communion (contra the contemporary “credible profession” view) see:
http://honest2blog.blogspot.com/2010/02/recovering-reformed-communion.html
http://honest2blog.blogspot.com/2010/04/recovering-reformed-communion-2.html

Since it was raised in the episode, I am kind of curious as to how low the bar ought to be for membership. I fully admit the distinction between requirements for office and those for members, and that we ought not to break the bruised reed or quench the smoking flax. But specifically, if there is a bar against ignorance and scandalousness (L. Cat. 173) and that the ignorant ought not be admitted to the table “until they receive instruction,” what level of knowledge should be required? At present, I’m inclined to say that in Presbyterian churches a working knowledge of the teaching of the Shorter Catechism (and not necessarily the Confession) would be the cognitive bar, at least as a general rule. Is that fair?